BEI and equity paper analyses | FINAL | Hurdle models

# Clean up dataframe to keep only meaningful vars and drop NA, ready for LM
tidy_df <- function(src_df, ct, f, drop_islands=TRUE) {
  clean_bei_df <- src_df %>%
    select(CT_UID, all_of(all.vars(f))) %>%
    drop_na() %>%
    units::drop_units()
  
  # Join geom from CT dataframe
  df <- ct %>%
    transmute(CT_UID = GeoUID) %>%
    inner_join(clean_bei_df, by="CT_UID")
  
  # Build neighborhood (with islands) and extract island IDs
  ct_nb <- poly2nb(df)
  
  if (drop_islands) {
    islands <- lapply(ct_nb, min) %>% lapply(function(e) e == 0) %>% unlist %>% which()

    # Cleanup subset DF to drop islands and NA
    df <- df %>%
      filter(!row_number() %in% islands) %>%
      mutate(ct_no = row_number()) # Add CT number, matching row number
  
    # Recompute neighborhood
    ct_nb <- poly2nb(df)
    
    # Clean up final dataframe (no island, no NA's, pure dataframe)
    clean_df <- df %>%
      as.data.frame() %>%
      select(CT_UID, ct_no, all_of(all.vars(f)))
  }

  nbw = nb2listw(ct_nb, zero.policy = !drop_islands)
  nbmatx = nb2mat(ct_nb, style = "B", zero.policy = !drop_islands)
  
  list(df=clean_df, nbmatx=nbmatx, nbw=nbw, island_dropped=drop_islands)
}

This document builds on BEI_equity_paper.Rmd doc, which started as an analysis for the equity paper and moved to an exploration of the best modeling framework (simple OLS, spatial auto-regressive linear regression, spatial random effect model and INLA) to assess the relation between interventions and equity metrics. The conclusions of this exploration led to the following decisions:

1. go with quintiles instead of absolute numbers (easier to interpret)
2. use [zero inflated] Poisson distribution where fit (ie Bike lane ratio)
3. use spaMM package to model association; INLA could be the focus of another methodological paper which would compare both approaches
4. use non-buffered dependent variable, as spatial dependency is already taken care of through the spatial random effect

This document contains the analyses to be included in the BEI and equity paper.

1 Proposal

1.1 Original grant proposal for Census tract level analyses

1.1.1 Objective 1: Socio-spatial inequalities in urban interventions:

• To test if urban interventions tend to be located in low SES neighborhoods (H1a); we will run the following model: \[Log(𝔼(UI_{𝑖} \mid X_{𝑖})) = \alpha + \beta_{1} * SES_{𝑖}\] a Poisson regression model with \(UI\) = the number of Urban Interventions between 2016 and 2021, \(SES\) = the socio-economic status of the census track at 2016.
• To test the reduction in socio-economic inequalities in urban conditions (e.g. length and type of bicycle lanes, NDVI) between 2006 and 2020 (H1b), we will run the following model: \[𝔼(UC_{ij} \mid X_{ij}) = \beta_{0j} + \beta_{1j} ∗ SES + \beta_{2j} ∗ Time + \beta_{3j} ∗ SES ∗ Time + \epsilon_{ij}\] a multilevel linear model with \(UC\) = the Urban condition, \(SES\) = the socio-economic status of the census track.

1.1.2 Objective 2: Examining causal pathways and directionality of intervention/gentrification relation:

• To test if urban interventions occur before gentrification or if gentrification occurs before the implementation of new urban interventions, we will run two models : (1) \[Logit(𝔼(G_{i} \mid X_{i})) = \alpha + \beta_{1} ∗ UI_{i} + + \beta_{2} ∗ PG_{i} + \beta ∗ X_{control_{i}}\] a logistic regression model among low SES census tracts (2006) with \(G\) = Gentrification between 2006 and 2016, \(UI\) = the number of Urban Interventions between 2001 and 2006, and \(PG\) = SES status 2006; and (2) \[Logit(𝔼(UI_{i} \mid X_{i})) = \alpha + \beta_{1} ∗ G_{i} + \beta_{2} ∗ UC_{i} + \beta ∗ X_{control_{i}}\] a Poisson regression model, with \(UI\) = the number of Urban Interventions between 2016 and 2023, \(G\) = Gentrification between 2006 and 2016, and \(UC\) = Urban Conditions in 2016.

1.2 Paper objective

We focus on obj #1: are urban interventions tend to be located in low SES neighborhoods. Here, the urban interventions considered are bike lanes and canopy/tree coverage and low SES ~ high Pampalon deprivation index. In a second step, we will look at the variations of UI and SES and their association.

Data extraction and pre-analyses for the paper looking at BEI and equity. BEI comprise bike lanes and canopy changes while equity is measured through Pampalon deprivation index. (Partially adapted from original work on BEI bike lanes – see bike_lane_stats.R and ReadMe.md.)

Paper is available here.

General processing steps:

• Get CT 2016 boundaries (from Cancensus API)
• Get BEI interventions (canopy / bike lanes) for the selected years (2011 / 2015 / 2016 / 2019)
• Compute changes between years
  • for the original CT boundaries
  • for buffered CTs (250 / 500 / 750m)

In a second phase, these BEI changes will be linked to Pampalon index for 2016 (and 2011 ?)

1.3 Revision history

UPDATE 2021-12-02 Following discussion with @Yan, add normalized bike line changes:

• by CT/buffer area
• by street length within CT/buffer

UPDATE 2021-12-08 Following discussion with @Yan

• Keep only normalized variation of bike lane length
• Reverse relation: BEI metric = f(Equity metric (Pampalon / gentrification))
• Display association at baseline, then add delta over time
• Canopy : distinguish between high and low canopy

UPDATE 2022-01-14 Following discussion with @Ruben and @Yan

• Test model with UC 2011 when modeling UI
• Models with random slope probably not pertinent (see model 6, section 7.1.6)
• Try to define Year variable as continuous instead of category in LME
• Check if range of wSCOREMAT matches theoretical range of x-axis in graph (-.2 >> .2), might ponder the magnitude of the observed trend
• Test three-way interaction instead of 2 times two-way interactions (interactions might be complicated to interpret…)
• For gentrification and multilevel model, use GEE (logit)

UPDATE 2022-02-10 Following gentrification meeting

• Add correlation matrix of SES variables (Caislin)
• Drop wSCORESOC, which does not capture equity dimension (Meghan) [replaced by visible minority]
• Paper focus should be on gentrification

UPDATE 2022-02-15

• Add spatial autocorrelation test (Moran’s I)
• Add Lagrange Multipliers to test best spatial model
• Add comparison of OLS/SAR/SEM models

UPDATE 2022-06-28

• Add categorical SES variables (instead of ordinal coding) to better explain the Q5 vs other effect (see Behzad and Yan’s comments); this is particularly true for bike lanes changes, as no significant effect found yet graph shows clearly a Q5 vs. other effect
• Build maps of SES (?) and BEI / BEC (might be better in ArcGIS)

UPDATE 2022-07-07

• Fix quintile computation (which was previously based on the whole CMA and now uses the actual AOI)
• Dropped a few useless chunks (mostly bike lane, no hurdle model)

1.4 A few references…

• General resources on GLMM
  • GLMM FAQ
• Count and rate models:
  • A tutorial on count regression and zero-altered count models for longitudinal substance use data
  • Regression Analyses of Counts and Rates: Poisson, Overdispersed Poisson, and Negative Binomial Models
  • The Analysis of Count Data: A Gentle Introduction to Poisson Regression and Its Alternatives
• Spatial models:
  • https://rspatial.org/raster/analysis/7-spregression.html
  • https://rpubs.com/quarcs-lab/tutorial-spatial-regression
  • https://www.r-bloggers.com/2019/09/spatial-regression-in-r-part-1-spamm-vs-glmmtmb/
  • https://crd230.github.io/lab8.html
  • http://labs.bio.unc.edu/Buckley/documents/AnselinIntroSpatRegres.pdf
• Interactions:
  • Decomposing, Probing, and Plotting Interactions in R
  • Sophisticated models in emmeans
  • R for Researchers: An Introduction
  • Recommendations for presenting analyses of effect modification and interaction
  • Testing interact terms

2 Built Environment Intervention Extraction

2.1 Bike lane changes

We use data categorized by Philippe Apparicio’s team who manually identified bike lanes for each census year since 1991. For this study, we limit ourselves to 2016, 2011 and 2006 census years.

On top of the original CT boundaries, three levels of buffer have been applied to the CT – 250m, 500m & 750m. Then the same series of processing steps (see above) have been applied to the buffers.

# Bike lanes, from Ph. Apparicio
reseau <- st_read(dsn="data/ReseauCyclableFinal.gdb", layer = "Reseau") # Already in NAD83 / MTM zone 8

## Reading layer `Reseau' from data source 
##   `/Users/benoit/WORKSPACE/gentrification_BEI_equity/data/ReseauCyclableFinal.gdb' 
##   using driver `OpenFileGDB'
## Simple feature collection with 82166 features and 72 fields
## Geometry type: GEOMETRY
## Dimension:     XYZ, XYZM
## Bounding box:  xmin: 266985.5 ymin: 5029251 xmax: 320986.1 ymax: 5062652
## z_range:       zmin: 0 zmax: 43
## m_range:       mmin: 0 mmax: 43
## Projected CRS: NAD83 / MTM zone 8

bike_lane <- reseau %>%
  filter(An2016 == 1 | An2011 == 1) %>%
  select(IdRte, ClsRte, Zone, starts_with("An"), starts_with("Typo_")) %>%
  st_cast("MULTILINESTRING") # Get rid of a few MULTICURVE geometries

# CT boundaries for Montreal
CT16 <- get_census(dataset='CA16', regions=list(CMA='24462'), level='CT', geo_format = "sf") %>%
  filter(Type == "CT") %>%
  mutate(interact_aoi = CD_UID %in% c(2466, 2465, 2458)) %>% # Flag Montréal island, Laval and the South shore (Longueuil, St-Lambert, Brossard)
  st_transform(st_crs(bike_lane))

## Reading geo data from local cache.

CT11 <- get_census(dataset='CA11', regions=list(CMA='24462'), level='CT', geo_format = "sf") %>%
  filter(Type == "CT") %>%
  st_transform(st_crs(bike_lane))

## Reading geo data from local cache.

compute_bikelane_by_area <- function(sf_areas, year_fld, typo_fld) {
  # Compute length of bike lanes within each area.
  # --
  # Parameters:
  #   - sf_areas: sf class object defining the areas of interest, must have a GeoUID field
  #   - year_fld: field name specifying the year of interest, e.g. An2016
  #   - typo_fld: field name specifying the typology for the year of interest, e.g. Typo_2016
  
  year_fld <- enquo(year_fld)
  typo_fld <- enquo(typo_fld)
  
  # Compute intersection of bike lanes with areas
  bk <- bike_lane %>%
    filter(!!year_fld == 1) %>%
    st_intersection(sf_areas) %>%
    mutate(bike_lane_length = st_length(.)) %>%
    as.data.frame() %>%
    group_by(GeoUID, !!typo_fld) %>%
    summarise(bike_lane_length = sum(bike_lane_length)) %>%
    ungroup() %>%
    pivot_wider(names_from = !!typo_fld, names_prefix = "Bike_class", names_sort = TRUE,
                values_from = bike_lane_length, values_fill = units::set_units(0, m)) %>%
    mutate(Bike_lane_total = units::set_units(rowSums(select(., starts_with("Bike_class"))), m))
  
  # Merge back into original sf_areas
  bk <- sf_areas %>%
    left_join(bk)
  
  # Replace NA by 0, which occur in Bike_class length
  bk[is.na(bk)] <- 0
  
  return(bk)
}

compute_streetlength_by_area <- function(sf_areas) {
  # Compute length of streets within each area.
  # --
  # Parameters:
  #   - sf_areas: sf class object defining the areas of interest, must have a GeoUID field

  # Compute intersection of streets with areas
  bk <- reseau  %>%
    st_cast("MULTILINESTRING") %>% # Get rid of a few MULTICURVE geometries
    st_intersection(sf_areas) %>%
    mutate(street_length = st_length(.)) %>%
    as.data.frame() %>%
    group_by(GeoUID) %>%
    summarise(street_length = sum(street_length)) %>%
    ungroup()
  
  # Merge back into original sf_areas
  bk <- sf_areas %>%
    mutate(shape_area_km2 = units::set_units(st_area(.), 'km^2')) %>%
    left_join(bk)
  
  # Replace NA by 0
  bk[is.na(bk)] <- 0
  
  return(bk)
}


# Compute year 2016 and year 2011 bike lanes within 2016 CTs
# NB: contrary to the original work, we keep the same area of reference, i.e. 2016
bike_lane_by_CT16 <- compute_bikelane_by_area(CT16, An2016, Typo_2016)
bike_lane_by_CT11 <- compute_bikelane_by_area(CT16, An2011, Typo_2011)
bike_lane_by_CT06 <- compute_bikelane_by_area(CT16, An2006, Typo_2006)

# Compute total street length within CT/buffer
street_length_by_CT16 <- compute_streetlength_by_area(CT16)

# Reorganize data to have all data in one dataframe
bike_lane_changes <- CT16 %>%
  left_join(select(as.data.frame(street_length_by_CT16), GeoUID, street_length, shape_area_km2), by="GeoUID") %>%
  left_join(select(as.data.frame(bike_lane_by_CT16), GeoUID, starts_with("Bike_")), by="GeoUID") %>%
  left_join(select(as.data.frame(bike_lane_by_CT11), GeoUID, starts_with("Bike_")), by="GeoUID", suffix=c(".2016ct", ".2011ct")) %>%
  left_join(select(as.data.frame(bike_lane_by_CT06), GeoUID, starts_with("Bike_")), by="GeoUID")

# Compute ratio of bike lane vs street length
bike_lane_changes <- bike_lane_changes %>%
  transmute(GeoUID = GeoUID,
            interact_aoi = interact_aoi,
            street_length = street_length,
            street_length.hm = street_length / 100, # in hectometers, can be kept as float (not a dependent variable following a Poisson distribution)
            Bike_lane_total.2016ct = Bike_lane_total.2016ct,
            Bike_lane_total.2011ct = Bike_lane_total.2011ct,
            Bike_lane_total.2006ct = Bike_lane_total,
            Bike_lane_total.hm.2016ct = as.integer(round(Bike_lane_total.2016ct/100)),
            Bike_lane_total.hm.2011ct = as.integer(round(Bike_lane_total.2011ct/100)),
            Bike_lane_total.hm.2006ct = as.integer(round(Bike_lane_total/100)),
            Bike_lane.by.street.2016ct = 100 * Bike_lane_total.2016ct / street_length, # In percents
            Bike_lane.by.street.2011ct = 100 * Bike_lane_total.2011ct / street_length,
            Bike_lane.by.street.2006ct = 100 * Bike_lane_total / street_length)

# Compute change between 2011 and 2016 (only for total bike lane length)
bike_lane_changes <- bike_lane_changes %>%
  mutate(Bike_lane_diff.2011.2016ct = Bike_lane_total.2016ct - Bike_lane_total.2011ct)

# Normalize bike lane change by (i) street length and (ii) area
bike_lane_changes <- bike_lane_changes %>%
  mutate(Bike_lane_diff.by.street.2011.2016ct = 100 * Bike_lane_diff.2011.2016ct / street_length)

# Save results
st_write(bike_lane_changes, dsn = "data/bike_length_changes.gpkg", delete_layer = TRUE)

## Deleting layer `bike_length_changes' using driver `GPKG'
## Writing layer `bike_length_changes' to data source 
##   `data/bike_length_changes.gpkg' using driver `GPKG'
## Writing 970 features with 15 fields and geometry type Multi Polygon.

# Clean up
rm(buf_CT16)
rm(bike_lane_by_CT11, bike_lane_by_CT16, bike_lane_by_CT06)
rm(street_length_by_CT16)

2.1.1 Illustration of bike lane metrics

Check output for one specific dataset (Census tracts 2016, no buffer)

2.1.1.1 Raw length

Bike lane length in 2016 within CTs, measured in meters

ggplot() +
   geom_sf(data=filter(bike_lane_changes, interact_aoi), mapping = aes(fill=as.numeric(Bike_lane_total.2016ct)), lwd=0) +
  scale_fill_continuous(name = "Total length (m)")+ 
  labs(title = "Length of bike lanes within 2016 CTs")

2.1.1.2 Absolute length change

Absolute bike lane length change between 2011 and 2016, in meters

ggplot() +
   geom_sf(data=filter(bike_lane_changes, interact_aoi), mapping = aes(fill=as.numeric(Bike_lane_diff.2011.2016ct)), lwd=0) +
  scale_fill_gradient2(name = "Length (m)")+ 
  labs(title = "Changes in bike lane between 2011 and 2016")

2.1.1.3 Normalized length change (by street)

Relative bike lane length change between 2011 and 2016, normalized by street length within CT in 2016, expressed in %

\[Variation = \frac{Bike Lane_{2016}}{Street Length_{2016}} - \frac{Bike Lane_{2011}}{Street Length_{2016}}\]

ggplot() +
   geom_sf(data=filter(bike_lane_changes, interact_aoi), mapping = aes(fill=as.numeric(Bike_lane_diff.by.street.2011.2016ct)), lwd=0) +
  scale_fill_gradient2(name = "Variation (%)")+ 
  labs(title = "Changes in bike lane between 2011 and 2016, normalized by street")

2.1.2 Basic stats on each layer

At the Census Tract level.

# CT level
ggplot(bike_lane_changes) +
  geom_histogram(aes(as.numeric(Bike_lane_diff.2011.2016ct)), binwidth = 250) + 
  xlab("Difference of bike lane length between 2016 and 2011 | CT level")

summary(bike_lane_changes$Bike_lane_diff.2011.2016ct)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -1377.7     0.0     0.0   262.1   189.7 14463.8

ggplot(bike_lane_changes) +
  geom_histogram(aes(as.numeric(Bike_lane_diff.by.street.2011.2016ct))) + 
  xlab("Difference of bike lane length between 2016 and 2011, normalized by street")

summary(bike_lane_changes$Bike_lane_diff.by.street.2011.2016ct)

##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.     NA's 
## -100.000    0.000    0.000    3.665    4.496  100.000      252

2.2 Canopy changes

Canopy changes is based on data produced by CMM, using multispectral aerial imagery and lidar. In order to sync the observations with the census years, we focus on 2011 and 2019 with one extra observation point in 2015.

The processing steps are similar to the ones for the bike lanes:

• Import the raster for each of the 3 years
• Compute proportion of canopy within each CT for the 3 years

# Codes du raster "espace vert"
# 0. No data (hors CMM)
# 1. NDVI < 0,3 et MNH < 3,0m = Minéral bas (route, stationnement, etc.)
# 2. NDVI < 0,3 et MNH ≥ 3,0m = Minéral haut (constructions)
# 3. NDVI ≥ 0,3 et MNH < 3,0m = Végétal bas (culture, gazon, etc.)
# 4. NDVI ≥ 0,3 et MNH ≥ 3,0m = Végétal haut (canopée)
# 5. Aquatique

# Load rasters into pg database for further processing
system('psql -d gentrif_bei -c "CREATE EXTENSION IF NOT EXISTS postgis"')
system('psql -d gentrif_bei -c "CREATE EXTENSION IF NOT EXISTS postgis_raster"')

if (nrow(dbGetQuery(con_bei, "SELECT 1 test WHERE to_regclass('canopee2019') IS NOT NULL;")) == 0) {
  system("raster2pgsql -s 32188 -I -C -M data/canopy/2019/*.tif -F -t 1000x1000 canopee2019 | psql -d gentrif_bei", intern = TRUE)
} else { message("PG Raster 'canopee2019' already imported") }

## PG Raster 'canopee2019' already imported

if (nrow(dbGetQuery(con_bei, "SELECT 1 test WHERE to_regclass('canopee2017') IS NOT NULL;")) == 0) {
  system("raster2pgsql -s 32188 -I -C -M data/canopy/2017/*.tif -F -t 1000x1000 canopee2017 | psql -d gentrif_bei", intern = TRUE)
} else { message("PG Raster 'canopee2017' already imported") }

## PG Raster 'canopee2017' already imported

if (nrow(dbGetQuery(con_bei, "SELECT 1 test WHERE to_regclass('canopee2015') IS NOT NULL;")) == 0) {
  system("raster2pgsql -s 32188 -I -C -M data/canopy/2015/*.tif -F -t 1000x1000 canopee2015 | psql -d gentrif_bei", intern = TRUE)
} else { message("PG Raster 'canopee2015' already imported") }

## PG Raster 'canopee2015' already imported

if (nrow(dbGetQuery(con_bei, "SELECT 1 test WHERE to_regclass('canopee2011') IS NOT NULL;")) == 0) {
  system("raster2pgsql -s 32188 -I -C -M data/canopy/2011/*.tif -F -t 1000x1000 canopee2011 | psql -d gentrif_bei", intern = TRUE)
} else { message("PG Raster 'canopee2011' already imported") }

## PG Raster 'canopee2011' already imported

# Resample to 10m as the original rasters have a 1m resolution, which is too high to allow for a swift processing
if (nrow(dbGetQuery(con_bei, "SELECT 1 test WHERE to_regclass('canopee2019_10m') IS NOT NULL;")) == 0) {
  system("gdal_translate -of GTiff PG:\"host=localhost dbname=gentrif_bei table=canopee2019 mode=2\" -r mode -tr 10 10 data/canopy/canopee2019_10m.tif")
  system("raster2pgsql -s 32188 -I -C -M data/canopy/canopee2019_10m.tif -F -t 100x100 canopee2019_10m | psql -d gentrif_bei")
} else { message("PG Raster 'canopee2019_10m' already imported") }

## PG Raster 'canopee2019_10m' already imported

if (nrow(dbGetQuery(con_bei, "SELECT 1 test WHERE to_regclass('canopee2017_10m') IS NOT NULL;")) == 0) {
  system("gdal_translate -of GTiff PG:\"host=localhost dbname=gentrif_bei table=canopee2017 mode=2\" -r mode -tr 10 10 data/canopy/canopee2017_10m.tif")
  system("raster2pgsql -s 32188 -I -C -M data/canopy/canopee2017_10m.tif -F -t 100x100 canopee2017_10m | psql -d gentrif_bei")
} else { message("PG Raster 'canopee2017_10m' already imported") }

## PG Raster 'canopee2017_10m' already imported

if (nrow(dbGetQuery(con_bei, "SELECT 1 test WHERE to_regclass('canopee2015_10m') IS NOT NULL;")) == 0) {
  system("gdal_translate -of GTiff PG:\"host=localhost dbname=gentrif_bei table=canopee2015 mode=2\" -r mode -tr 10 10 data/canopy/canopee2015_10m.tif")
  system("raster2pgsql -s 32188 -I -C -M data/canopy/canopee2015_10m.tif -F -t 100x100 canopee2015_10m | psql -d gentrif_bei")
} else { message("PG Raster 'canopee2015_10m' already imported") }

## PG Raster 'canopee2015_10m' already imported

if (nrow(dbGetQuery(con_bei, "SELECT 1 test WHERE to_regclass('canopee2011_10m') IS NOT NULL;")) == 0) {
  system("gdal_translate -of GTiff PG:\"host=localhost dbname=gentrif_bei table=canopee2011 mode=2\" -r mode -tr 10 10 data/canopy/canopee2011_10m.tif")
  system("raster2pgsql -s 32188 -I -C -M data/canopy/canopee2011_10m.tif -F -t 100x100 canopee2011_10m | psql -d gentrif_bei")
} else { message("PG Raster 'canopee2011_10m' already imported") }

## PG Raster 'canopee2011_10m' already imported

# Push CT16 to pg
if (nrow(dbGetQuery(con_bei, "SELECT 1 test WHERE to_regclass('ct16') IS NOT NULL;")) == 0) {
  CT16 %>%
    st_transform(crs = 32188) %>%
    st_write(con_bei, "ct16",
             layer_options = c("OVERWRITE=yes", "LAUNDER=true", "SPATIAL_INDEX=gist", "GEOMETRY_NAME=geom"))
  system("psql -d gentrif_bei -c 'CREATE INDEX ON  ct16 USING gist (geometry)'")
} else { message("PG Layer CT16 already imported") }

## PG Layer CT16 already imported

WITH cnt19 AS (
    SELECT "GeoUID", "Population"
        ,(pvc).value, SUM((pvc).count) As total
    FROM (SELECT "GeoUID", "Population"
            ,ST_ValueCount(ST_Clip(rast, geometry)) As pvc
        FROM canopee2019_10m
        JOIN ct16 ON ST_Intersects(geometry, rast)
    ) As foo
    GROUP BY "GeoUID", "Population", (pvc).value
),
canopee19 AS (
    SELECT "GeoUID"
        ,round(.1*.1 * sum(total) FILTER (WHERE value in (3, 4))) AS area_esp_vert_2019 -- area expressed in hectares
        ,round(100. * sum(total) FILTER (WHERE value in (3, 4)) / sum(total), 1) AS pct_esp_vert_2019
        ,round(.1*.1 * sum(total) FILTER (WHERE value = 4)) AS area_esp_vert_high_2019
        ,round(100. * sum(total) FILTER (WHERE value = 4) / sum(total), 1) AS pct_esp_vert_high_2019
    FROM cnt19
    WHERE value > 0 -- discard no data, including postgis raster no data
    GROUP BY "GeoUID", "Population"
),
cnt17 AS (
    SELECT "GeoUID", "Population"
        ,(pvc).value, SUM((pvc).count) As total
    FROM (SELECT "GeoUID", "Population"
            ,ST_ValueCount(ST_Clip(rast, geometry)) As pvc
        FROM canopee2017_10m
        JOIN ct16 ON ST_Intersects(geometry, rast)
    ) As foo
    GROUP BY "GeoUID", "Population", (pvc).value
),
canopee17 AS (
    SELECT "GeoUID"
        ,round(.1*.1 * sum(total) FILTER (WHERE value in (3, 4))) AS area_esp_vert_2017
        ,round(100. * sum(total) FILTER (WHERE value in (3, 4)) / sum(total), 1) AS pct_esp_vert_2017
        ,round(.1*.1 * sum(total) FILTER (WHERE value = 4)) AS area_esp_vert_high_2017
        ,round(100. * sum(total) FILTER (WHERE value = 4) / sum(total), 1) AS pct_esp_vert_high_2017
    FROM cnt17
    WHERE value > 0 -- discard no data, including postgis raster no data
    GROUP BY "GeoUID", "Population"
),
cnt15 AS (
    SELECT "GeoUID", "Population"
        ,(pvc).value, SUM((pvc).count) As total
    FROM (SELECT "GeoUID", "Population"
            ,ST_ValueCount(ST_Clip(rast, geometry)) As pvc
        FROM canopee2015_10m
        JOIN ct16 ON ST_Intersects(geometry, rast)
    ) As foo
    GROUP BY "GeoUID", "Population", (pvc).value
),
canopee15 AS (
    SELECT "GeoUID"
        ,round(.1*.1 * sum(total) FILTER (WHERE value in (3, 4))) AS area_esp_vert_2015
        ,round(100. * sum(total) FILTER (WHERE value in (3, 4)) / sum(total), 1) AS pct_esp_vert_2015
        ,round(.1*.1 * sum(total) FILTER (WHERE value = 4)) AS area_esp_vert_high_2015
        ,round(100. * sum(total) FILTER (WHERE value = 4) / sum(total), 1) AS pct_esp_vert_high_2015
    FROM cnt15
    WHERE value > 0 -- discard no data, including postgis raster no data
    GROUP BY "GeoUID", "Population"
),
cnt11 AS (
    SELECT "GeoUID", "Population"
        ,(pvc).value, SUM((pvc).count) As total
    FROM (SELECT "GeoUID", "Population"
            ,ST_ValueCount(ST_Clip(rast, geometry)) As pvc
        FROM canopee2011_10m
        JOIN ct16 ON ST_Intersects(geometry, rast)
    ) As foo
    GROUP BY "GeoUID", "Population", (pvc).value
),
canopee11 AS (
    SELECT "GeoUID"
        ,round(.1*.1 * sum(total) FILTER (WHERE value in (3, 4))) AS area_esp_vert_2011
        ,round(100. * sum(total) FILTER (WHERE value in (3, 4)) / sum(total), 1) AS pct_esp_vert_2011
        ,round(.1*.1 * sum(total) FILTER (WHERE value = 4)) AS area_esp_vert_high_2011
        ,round(100. * sum(total) FILTER (WHERE value = 4) / sum(total), 1) AS pct_esp_vert_high_2011
    FROM cnt11
    WHERE value > 0 -- discard no data, including postgis raster no data
    GROUP BY "GeoUID", "Population"
)
SELECT "GeoUID"
    ,round((st_area(geometry) / 10000)::numeric, 1) ct_area_h -- CT area in hectares
    ,COALESCE(area_esp_vert_2011, 0) area_esp_vert_2011
    ,coalesce(area_esp_vert_high_2011, 0) area_esp_vert_high_2011
    ,coalesce(pct_esp_vert_high_2011, 0) pct_esp_vert_high_2011
    ,coalesce(pct_esp_vert_2011, 0) pct_esp_vert_2011
    ,COALESCE(area_esp_vert_2015, 0) area_esp_vert_2015
    ,coalesce(area_esp_vert_high_2015, 0) area_esp_vert_high_2015
    ,coalesce(pct_esp_vert_high_2015, 0) pct_esp_vert_high_2015
    ,coalesce(pct_esp_vert_2015, 0) pct_esp_vert_2015
    ,COALESCE(area_esp_vert_2017, 0) area_esp_vert_2017
    ,coalesce(area_esp_vert_high_2017, 0) area_esp_vert_high_2017
    ,coalesce(pct_esp_vert_high_2017, 0) pct_esp_vert_high_2017
    ,coalesce(pct_esp_vert_2017, 0) pct_esp_vert_2017
    ,COALESCE(area_esp_vert_2019, 0) area_esp_vert_2019
    ,coalesce(area_esp_vert_high_2019, 0) area_esp_vert_high_2019
    ,coalesce(pct_esp_vert_high_2019, 0) pct_esp_vert_high_2019
    ,coalesce(pct_esp_vert_2019, 0) pct_esp_vert_2019
FROM ct16
FULL JOIN canopee19 USING ("GeoUID")
FULL JOIN canopee17 USING ("GeoUID")
FULL JOIN canopee15 USING ("GeoUID")
FULL JOIN canopee11 USING ("GeoUID");

2.3 Pampalon index

Get it here

pampalon <- read.xlsx("data/Canada2016Pampalon/A-MSDIData_Can2016_eng/1. EquivalenceTableCanada2016_ENG.xlsx", sheet = 2) %>%
  mutate(DA = as.character(DA)) %>%
  select(DA, SCOREMAT, SCORESOC)

# 2016 DA boundaries for Montreal
DA16 <- get_census(dataset='CA16', regions=list(CMA='24462'), level='DA', geo_format = "sf") %>%
  filter(Type == "DA") %>%
  st_transform(st_crs(bike_lane))

## Reading geo data from local cache.

pampalon <- DA16 %>%
  inner_join(pampalon, by = c("GeoUID" = "DA")) %>%
  as.data.frame()

# Get Pampalon 2006
pampalon06 <- read.xlsx("data/Canada2006Pampalon/A-MSDIData_Can2006_eng/1. CorrespondenceTable_Can2006_eng.xlsx", sheet = 2) %>%
  mutate(DA = as.character(DA)) %>%
  select(DA, DAPOP2006, SCOREMAT, SCORESOC)

# Get LUT DA2006 <-> DA2011 from StatCan
lut_da.1 <- read.csv("data/2011_92-156_DA_AD_txt/2011_92-156_DA_AD.txt", colClasses = "character", 
                     header = FALSE, col.names = c("DAUID2011.ADIDU2011", "DAUID2006.ADIDU2006", "DBUID2011", "DA_rel_flag")) %>%
  select(!c(DBUID2011, DA_rel_flag)) %>%
  unique()

# Link Pampalon 2011 to LUT and compute weighted mean of scores of Pampalon 2011
# NB: population numbers will diverge from  reality when more than one DA is merged into one DA of next census
pampalon06.11 <- pampalon06 %>%
  inner_join(lut_da.1, by = c("DA" = "DAUID2006.ADIDU2006")) %>%
  group_by(DAUID2011.ADIDU2011) %>%
  summarise(pop2006 = sum(DAPOP2006),
            SCOREMAT.06 = weighted.mean(SCOREMAT, DAPOP2006, na.rm = TRUE),
            SCORESOC.06 = weighted.mean(SCORESOC, DAPOP2006, na.rm = TRUE))

# Get Pampalon 2011
pampalon11 <- read.xlsx("data/Canada2011Pampalon/A-MSDIData_Can2011_eng/1. CorrespondenceTable_Can2011_eng.xlsx", sheet = 2) %>%
  mutate(DA = as.character(DA)) %>%
  select(DA, DAPOP2011, SCOREMAT, SCORESOC)

# Get LUT DA2011 <-> DA2016 from StatCan
lut_da <- read.csv("data/2016_92-156_DA_AD_csv/2016_92-156_DA_AD.csv", colClasses = "character") %>%
  select(!c(DBUID2016.IDIDU2016, DA_rel_flag.AD_ind_rel)) %>%
  unique()

# Link Pampalon 2011 to LUT, then to Pampalon 06 and finally compute weighted mean of scores of Pampalon 2011
pampalon11.16 <- pampalon11 %>%
  inner_join(lut_da, by = c("DA" = "DAUID2011.ADIDU2011")) %>%
  left_join(pampalon06.11, by =c("DA" = "DAUID2011.ADIDU2011")) %>%
  group_by(DAUID2016.ADIDU2016) %>%
  summarise(pop2011 = sum(DAPOP2011),
            SCOREMAT = weighted.mean(SCOREMAT, DAPOP2011, na.rm = TRUE),
            SCORESOC = weighted.mean(SCORESOC, DAPOP2011, na.rm = TRUE),
            SCOREMAT.06 = weighted.mean(SCOREMAT.06, pop2006, na.rm = TRUE),
            SCORESOC.06 = weighted.mean(SCORESOC.06, pop2006, na.rm = TRUE),
            pop2006 = sum(pop2006))

# Then link Pampalon 2011 to 2016
pampalon <- pampalon %>%
  left_join(pampalon11.16, by = c("GeoUID" = "DAUID2016.ADIDU2016"), suffix = c(".16", ".11"))

# Aggregate at the CT level
pampalon_CT <- pampalon %>%
  group_by(CT_UID) %>%
  summarise(wSCOREMAT.2016 = weighted.mean(SCOREMAT.16, Population, na.rm = TRUE),
            wSCORESOC.2016 = weighted.mean(SCORESOC.16, Population, na.rm = TRUE),
            wSCOREMAT.2011 = weighted.mean(SCOREMAT.11, pop2011, na.rm = TRUE),
            wSCORESOC.2011 = weighted.mean(SCORESOC.11, pop2011, na.rm = TRUE),
            wSCOREMAT.2006 = weighted.mean(SCOREMAT.06, pop2006, na.rm = TRUE),
            wSCORESOC.2006 = weighted.mean(SCORESOC.06, pop2006, na.rm = TRUE))

# Clean up
rm(lut_da, lut_da.1, pampalon11.16, pampalon06.11, pampalon11, pampalon06)

# Display map
.pampalon_CT_geom <- CT16 %>%
  left_join(pampalon_CT, by = c("GeoUID" = "CT_UID")) %>%
  filter(interact_aoi)

.pampalon_data <- bi_class(.pampalon_CT_geom, x = wSCOREMAT.2016, y = wSCORESOC.2016, style = "quantile", dim = 3)

## Warning in classInt::classIntervals(bins_x, n = dim, style = "quantile"): var
## has missing values, omitted in finding classes

## Warning in classInt::classIntervals(bins_y, n = dim, style = "quantile"): var
## has missing values, omitted in finding classes

.map <- ggplot() + 
  geom_sf(data = .pampalon_data, mapping = aes(fill = bi_class), color = "white", size = 0.1, show.legend = FALSE) +
  bi_scale_fill(pal = "DkBlue", dim = 3) +
  labs(title = "Pampalon: material and social deprivation index") + 
  theme(panel.background = element_rect(fill = "white"),
        #axis.ticks = element_blank(),
        #axis.text = element_blank(),
        panel.grid = element_line(color = "darkgray", size = 0.2))
.legend <- bi_legend(pal = "DkBlue",
                    dim = 3,
                    xlab = "Material ",
                    ylab = "Social ",
                    size = 8)
ggdraw() +
  draw_plot(.map, 0, 0, 1, 1) +
  draw_plot(.legend, 0.1, .7, 0.2, 0.2)

2.4 Gentrification

Using Ding metric computed on 5 year span.

# Load gentrified CTs, 5 year span (from repo gentrification_metrics)
ding <- list()
ding[["2016"]] <- st_read("data/gentrified_5years.gpkg", "gentrified_ding_16", quiet=TRUE) %>%
  filter(cma_uid_16 == "24462") %>%
  st_transform(st_crs(bike_lane))
ding[["2011"]] <- st_read("data/gentrified_5years.gpkg", "gentrified_ding_11", quiet=TRUE) %>%
  filter(cma_uid_11 == "24462") %>%
  st_transform(st_crs(bike_lane))
ding[["2006"]] <- st_read("data/gentrified_5years.gpkg", "gentrified_ding_06", quiet=TRUE) %>%
  filter(cma_uid_06 == "24462") %>%
  st_transform(st_crs(bike_lane))

.ding_map <- ding[["2016"]] %>%
  left_join(select(as.data.frame(CT16), GeoUID, interact_aoi), by = c("ct_uid_16" = "GeoUID")) %>%
  filter(interact_aoi)

ggplot(data = .ding_map) + 
  geom_sf(aes(fill = gentrified_2016_2011, colour=gentrifiable_2011)) +
  scale_fill_manual(values = c("gray", "red", "darkgray"), name = "Gentrified in 2016") +
  scale_colour_manual(values = c("darkgray", "darkred", "darkgray"), name = "Gentrifiable in 2011") +
  labs(title = "Census tract gentrification status in 2016")

2.5 Equity metrics | low-income population and visible minority

Introduced here as a proposition, nothing acted (2022-02-04)

# Visible Minority
# - v_CA16_3954: Total - Visible minority for the population in private households - 25% sample data (Total)
# - v_CA16_3957: Total visible minority population (Total)

# Low income (LIM-AT)
# - v_CA16_2540: Prevalence of low income based on the Low-income measure, after tax (LIM-AT) (%) (Total)
equity_ct16 <- get_census(dataset='CA16', regions=list(CMA='24462'), level='CT', geo_format = "sf",
                          vectors = c("v_CA16_3954", "v_CA16_3957", "v_CA16_2540")) %>%
  filter(Type == "CT") %>%
  transmute(CT_UID = GeoUID,
            vis_minority_2016 = `v_CA16_3957: Total visible minority population` / `v_CA16_3954: Total - Visible minority for the population in private households - 25% sample data` * 100,
            low_income_2016 = `v_CA16_2540: Prevalence of low income based on the Low-income measure, after tax (LIM-AT) (%)`)

## Reading vectors data from local cache.

## Reading geo data from local cache.

# Visible Minority
# - v_CA11N_457: CA 2011 NHS, Total population in private households by visible minority (Total)
# - v_CA11N_460: CA 2011 NHS, Total population in private households by visible minority, Total visible minority population (Total)

# Low income (LIM-AT)
# - v_CA11N_2606: CA 2011 NHS, Prevalence of low income in 2010 based on after-tax low-income measure % (Total)
equity_ct11 <- get_census(dataset='CA11', regions=list(CMA='24462'), level='CT', geo_format = "sf",
                          vectors = c("v_CA11N_457", "v_CA11N_460", "v_CA11N_2606")) %>%
  filter(Type == "CT") %>%
  transmute(CT_UID = GeoUID,
            vis_minority_2011 = `v_CA11N_460: Total visible minority population` / `v_CA11N_457: Total population in private households by visible minority` * 100,
            low_income_2011 = `v_CA11N_2606: Prevalence of low income in 2010 based on after-tax low-income measure %`)

## Reading vectors data from local cache.
## Reading geo data from local cache.

# Visible Minority
# - v_CA06_1302: Total population by visible minority groups
# - v_CA06_1303: Total population by visible minority groups, Total visible minority population

# Low income (LIM-AT)
# - v_TX2006_551: After-tax low income status of tax filers and dependents (census family low income measure, CFLIM-AT) for couple and lone parent families by family composition, 2006 | All family units | Persons in Low Income | % - Total
equity_ct06 <- get_census(dataset='CA06', regions=list(CMA='24462'), level='CT', geo_format = "sf",
                          vectors = c("v_CA06_1302", "v_CA06_1303", "v_TX2006_551")) %>%
  filter(Type == "CT") %>%
  transmute(CT_UID = GeoUID,
            vis_minority_2006 = `v_CA06_1303: Total visible minority population` / `v_CA06_1302: Total population by visible minority groups - 20% sample data` * 100,
            low_income_2006 = `v_TX2006_551: % - Total`)

## Reading vectors data from local cache.
## Reading geo data from local cache.

equity_ct <- st_join(equity_ct16, equity_ct11, left=TRUE, largest=TRUE, suffix=c("", "_2011")) %>% # join on largest overlap, to overcome mismatch in CT UID
  st_join(equity_ct06, left=TRUE, largest=TRUE, suffix=c("", "_2006")) %>%
  data.frame()

## Warning: attribute variables are assumed to be spatially constant throughout all
## geometries

## Warning: attribute variables are assumed to be spatially constant throughout all
## geometries

# cleanup
rm(equity_ct11, equity_ct16, equity_ct06)

# Display map
.equity_CT_geom <- CT16 %>%
  left_join(equity_ct, by = c("GeoUID" = "CT_UID")) %>%
  filter(interact_aoi)

.equity_data <- bi_class(.equity_CT_geom, x = vis_minority_2016, y = low_income_2016, style = "quantile", dim = 3)

## Warning in classInt::classIntervals(bins_x, n = dim, style = "quantile"): var
## has missing values, omitted in finding classes

## Warning in classInt::classIntervals(bins_y, n = dim, style = "quantile"): var
## has missing values, omitted in finding classes

.map <- ggplot() + 
  geom_sf(data = .equity_data, mapping = aes(fill = bi_class), color = "white", size = 0.1, show.legend = FALSE) +
  bi_scale_fill(pal = "Brown", dim = 3) +
  labs(title = "Equity metrics: % of visible minority and % of low-income household") + 
  theme(panel.background = element_rect(fill = "white"),
        #axis.ticks = element_blank(),
        #axis.text = element_blank(),
        panel.grid = element_line(color = "darkgray", size = 0.2))
.legend <- bi_legend(pal = "Brown",
                    dim = 3,
                    xlab = "Vis. Minority ",
                    ylab = "Low-Income ",
                    size = 8)
ggdraw() +
  draw_plot(.map, 0, 0, 1, 1) +
  draw_plot(.legend, 0.1, .7, 0.2, 0.2)

2.6 Build complete dataset

All variables + outcome linked at the CT level + quintiles of SES variables

.bike_lane_changes <- bike_lane_changes %>%
  as.data.frame() %>%
  select(GeoUID, starts_with("street_length"), ends_with("ct", ignore.case = FALSE)) %>%
  select(GeoUID, starts_with("street_length"), starts_with("Bike_lane")) # Drop individual category lane length

bei_df <- CT16 %>%
  as.data.frame() %>%
  transmute(CT_UID = GeoUID,
            CD_UID = CD_UID,
            CSD_UID = CSD_UID,
            interact_aoi = interact_aoi,
            zone = case_when(CD_UID == "2466" ~ "Montreal",
                             CD_UID == "2458" ~ "Longueuil",
                             CD_UID == "2465" ~ "Laval",
                             TRUE ~ "Other"),
            Population = Population) %>%
  left_join(pampalon_CT, by="CT_UID") %>%
  left_join(select(as.data.frame(ding$`2016`), ct_uid_16, starts_with("gentrif")), by=c("CT_UID" = "ct_uid_16")) %>%
  left_join(select(as.data.frame(ding$`2011`), ct_uid_11, starts_with("gentrif")), by=c("CT_UID" = "ct_uid_11")) %>%
  left_join(select(as.data.frame(ding$`2006`), ct_uid_06, starts_with("gentrif")), by=c("CT_UID" = "ct_uid_06")) %>%
  left_join(select(as.data.frame(equity_ct), !c("geometry", "CT_UID_2011", "CT_UID_2006")), by="CT_UID") %>%
  left_join(.bike_lane_changes, by=c("CT_UID" = "GeoUID")) %>%
  left_join(as.data.frame(rename_with(esp_vert_ct, ~ paste0(., "ct"))), by=c("CT_UID" = "GeoUIDct")) %>%
  # Compute quintile of SES variables
  mutate(wSCOREMAT.2006.Q = ntile(wSCOREMAT.2006, 5),
         wSCOREMAT.2011.Q = ntile(wSCOREMAT.2011, 5),
         wSCOREMAT.2016.Q = ntile(wSCOREMAT.2016, 5),
         low_income_2006.Q = ntile(low_income_2006, 5),
         low_income_2011.Q = ntile(low_income_2011, 5),
         low_income_2016.Q = ntile(low_income_2016, 5),
         vis_minority_2006.Q = ntile(vis_minority_2006, 5),
         vis_minority_2011.Q = ntile(vis_minority_2011, 5),
         vis_minority_2016.Q = ntile(vis_minority_2016, 5)) %>%
  units::drop_units()
  
  
head(bei_df)

write.csv(bei_df, "data/_results/bei_equity.csv", na="", row.names = FALSE)

# keep only interact CT 
# UPDATE 2022-07-07 ##########
# and recompute quintiles for the new AOI
bei_df_aoi <- filter(bei_df, interact_aoi) %>%
  mutate(wSCOREMAT.2006.Q = ntile(wSCOREMAT.2006, 5),
         wSCOREMAT.2011.Q = ntile(wSCOREMAT.2011, 5),
         wSCOREMAT.2016.Q = ntile(wSCOREMAT.2016, 5),
         low_income_2006.Q = ntile(low_income_2006, 5),
         low_income_2011.Q = ntile(low_income_2011, 5),
         low_income_2016.Q = ntile(low_income_2016, 5),
         vis_minority_2006.Q = ntile(vis_minority_2006, 5),
         vis_minority_2011.Q = ntile(vis_minority_2011, 5),
         vis_minority_2016.Q = ntile(vis_minority_2016, 5))

Included variables:

• Census Tracts variables
  • CT_UID: 2016 Census Tract ID
  • CD_UID: 2016 Census Division
  • CSD_UID: 2016 Census Subdivision
  • interact_aoi: Does CT belong to INTERACT study area?
  • zone: Montreal / Laval / Longueuil, etc. / Other
  • Population: 2016 Population within CT
  • ct_area_m2ct: Area of CT, in square meters
• Gentrification metrics
  • gentrified_2016_2011: Is the CT gentrified in 2016?
  • gentrifiable_2011: Is the CT candidate to gentrification in 2011?
  • gentrified_2011_2006: Is the CT gentrified in 2011
  • gentrifiable_2006: Is the CT candidate to gentrification in 2006
  • gentrified_2006_2001: Is the CT gentrified in 2006
  • gentrifiable_2001: Is the CT candidate to gentrification in 2001
• Pampalon’s metrics
  • wSCORESOC.2016: Social deprivation index in 2016 (population weighted)
  • wSCOREMAT.2016: Material deprivation index in 2016 (population weighted)
  • wSCOREMAT.2016.Q: Quintile of material deprivation index in 2016 (population weighted)
  • wSCORESOC.2011: Social deprivation index in 2011 (population weighted)
  • wSCOREMAT.2011: Material deprivation index in 2011 (population weighted)
  • wSCOREMAT.2011.Q: Quintile of aterial deprivation index in 2011 (population weighted)
  • wSCORESOC.2006: Social deprivation index in 2006 (population weighted)
  • wSCOREMAT.2006: Material deprivation index in 2006 (population weighted)
  • wSCOREMAT.2006.Q: Quintile of material deprivation index in 2006 (population weighted)
• Social profile
  • vis_minority_2016: % of visible minority in CT 2016
  • vis_minority_2016.Q: Quintile of % of visible minority in CT 2016
  • low_income_2016: prevalence of low income in CT 2016
  • low_income_2016.Q: Quintile of prevalence of low income in CT 2016
  • vis_minority_2011: % of visible minority in CT 2011
  • vis_minority_2011.Q: Quintile of % of visible minority in CT 2011
  • low_income_2011: prevalence of low income in CT 2011
  • low_income_2011.Q: Quintile of prevalence of low income in CT 2011
  • vis_minority_2006: % of visible minority in CT 2006
  • vis_minority_2006.Q: Quintile of % of visible minority in CT 2006
  • low_income_2006: prevalence of low income in CT 2006
  • low_income_2006.Q: Qintile of prevalence of low income in CT 2006
• Bike lane density
  • Bike_lane_total.{2016|2011}ct: total length of bike lanes, in 2016 or 2011, within CT
  • Bike_lane_total.hm.{2016|2011}ct: total length of bike lanes, in hectometers (as integers), in 2016 or 2011, within CT
  • Bike_lane.by.street.{2016|2011}ct: % of bike lanes compared to streets, in 2016 or 2011, within CT
  • Bike_lane_diff.2011.2016ct: change in total length of bike lanes between 2011 and 2016, within CT
  • Bike_lane_diff.by.street.2011.2016ct: change in total length of bike lanes between 2011 and 2011, normalized by street length, within CT
  • Bike_lane_diff.by.area.2011.2016ct: change in total length of bike lanes between 2011 and 2011, normalized by area, within CT
• Green spaces
  • area_esp_vert_{2011|2015|2019}ct: area of green space in 2011, 2015 or 2019 within CT (in hectares)
  • area_esp_vert_high_{2011|2015|2019}ct: same as above, except for trees (high canopy)
  • pct_esp_vert_{2011|2015|2019}ct: % of green space in 2011, 2015 or 2019 within CT
  • pct_esp_vert_high_{2011|2015|2019}ct: same as above, except for trees (high canopy)
  • pct_esp_vert_diff{2011|2015}.{2015|2019}ct: change in % of green space between 2011 and 2015, 2011 and 2019 as well as 2011 and 2019, within CT

3 Preliminary analyses

INTERACT study area ~ Montréal, Laval, Longueuil, Brossard, St-Lambert

3.1 SES variable distribution

.bei_df_long <- bei_df_aoi %>% 
  select(CT_UID, CD_UID, starts_with("wSCORE")) %>%
  select(!ends_with('.Q')) %>%
  pivot_longer(!c(CT_UID, CD_UID))

ggplot(.bei_df_long, aes(value)) +
  geom_histogram() + 
  facet_wrap(~name) #, scales = "free")

## Warning: Removed 86 rows containing non-finite values (stat_bin).

.bei_df_long <- bei_df_aoi %>%
  select(CT_UID, CD_UID, starts_with("vis_minority"), starts_with("low_income")) %>%
  select(!ends_with('.Q')) %>%
  pivot_longer(!c(CT_UID, CD_UID))

ggplot(.bei_df_long, aes(value)) +
  geom_histogram() + 
  facet_wrap(~name) #, scales = "free")

## Warning: Removed 85 rows containing non-finite values (stat_bin).

.bei_df_long <- bei_df_aoi %>%
  select(CT_UID, CD_UID, starts_with("gentrif")) %>%
  select(!ends_with('.Q')) %>%
  pivot_longer(!c(CT_UID, CD_UID))

ggplot(.bei_df_long, aes(value)) +
  geom_bar() + 
  facet_wrap(~name) #, scales = "free", ncol = 3)

3.2 BEI variable distributions

3.2.1 Absolute values

.bei_df_long <- bei_df_aoi %>% 
  filter(interact_aoi) %>%
  select(CT_UID, CD_UID, matches("^Bike_lane_total.*ct$"), matches("^area_esp_vert.*ct$")) %>%
  pivot_longer(!c(CT_UID, CD_UID))

ggplot(.bei_df_long, aes(value)) +
  geom_histogram() + 
  facet_wrap(~name, scales = "free", ncol = 4)

3.2.2 Relative values

.bei_df_long <- bei_df_aoi %>% 
  filter(interact_aoi) %>%
  select(CT_UID, CD_UID, matches("^Bike_lane.by.*ct$"), matches("^pct_esp_vert.*ct$")) %>%
  pivot_longer(!c(CT_UID, CD_UID))

ggplot(.bei_df_long, aes(value)) +
  geom_histogram() + 
  facet_wrap(~name, scales = "free", ncol = 3)

4 Association between SES and Urban Conditions at baseline (2011)

Looking at objective #1: do urban interventions tend to be located in low SES neighborhoods?. We look at \[Urban Condition_{2011} = f(SES_{2011})\] as well as \[Urban Condition_{2011} = f(Gentrification_{2011 \to 2016})\]

Here \(UrbanCondition\) means the state of the urban environment features, such as length of bike lanes, greenness coverage, etc. at one specific moment. This needs to be distinguished from \(UrbanIntervention\), which accounts for the changes in the \(UrbanConditions\) between two years (see below).

We fit LMM models, with spatial random effect using spaMM package.

4.1 UC vs Pampalon | material

4.1.1 Bike lane length (hurdle)

Bike lane ratio to streets at the Census tract level. We use an offset, as explained in Anderson’s presentation, to handle the denominator and model the Bike lane length in hectometers using a Poisson distribution.

Resorting to a hurdle model, to accommodate the zero-inflated distribution.

f <- Bike_lane_total.hm.2011ct ~ wSCOREMAT.2011.Q + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

# Zero model
res.lmm.zero <- fitme(I(Bike_lane_total.hm.2011ct != 0) ~ wSCOREMAT.2011.Q + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.zero, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2011ct != 0) ~ wSCOREMAT.2011.Q + offset(log(street_length.hm)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                  Estimate Cond. SE t-value   p-value
## (Intercept)       -2.3714  0.36381  -6.518 7.111e-11
## wSCOREMAT.2011.Q  -0.2359  0.09349  -2.523 1.164e-02
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1377511 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  1.489  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                       logLik
## p_v(h) (marginal L): -354.34

ci.lmm.0 <- confint(res.lmm.zero, 'wSCOREMAT.2011.Q')

## lower wSCOREMAT.2011.Q upper wSCOREMAT.2011.Q 
##            -0.44869647            -0.04680899

res.lmm.0 <- update(res.lmm.zero, . ~ . -wSCOREMAT.2011.Q)
LRT(res.lmm.0, res.lmm.zero)

##      chi2_LR df    p_value
## p_v 6.028834  1 0.01407403

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.zero, plot = F)
  plot(simout, title = "DHARMa residual | Logit")
}

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2011ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2011ct ~ wSCOREMAT.2011.Q + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2011ct ~ wSCOREMAT.2011.Q + offset(log(street_length.hm)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                  Estimate Cond. SE t-value p-value
## (Intercept)      -2.04308  0.09569 -21.351 0.00000
## wSCOREMAT.2011.Q -0.06073  0.02808  -2.163 0.03058
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1340074 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.3915  
## # of obs: 469; # of groups: ct_no, 469 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1735.752

ci.lmm.cnt <- confint(res.lmm.cnt, 'wSCOREMAT.2011.Q')

## lower wSCOREMAT.2011.Q upper wSCOREMAT.2011.Q 
##           -0.116508140           -0.005344248

res.lmm.0 <- update(res.lmm.cnt, . ~ . -wSCOREMAT.2011.Q)
LRT(res.lmm.0, res.lmm.cnt)

##      chi2_LR df    p_value
## p_v 4.616437  1 0.03166695

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.cnt, plot = F)
  plot(simout, title = "DHARMa residual | Count (truncated Poisson)")
}

# AIC
AIC(res.lmm.zero)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.zero$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4188.184

Interpretation of the wSCOREMAT.2011.Q coefficient (significant in both sub-models): - we have \(e^{-0.236}\) = 0.79 (95%CI: 0.638 – 0.954), which means each increase of 1 quintile in the Material Score 2011 leads to a 21% decrease the chance of having a bicycle lane in the CT - we have \(e^{-0.061}\) = 0.941 (95%CI: 0.89 – 0.995), which means in CTs with bike lanes, each increase of 1 quintile in the Material Score 2011 leads to a 5.9% decrease the ratio of bike lanes to street in 2011.

4.1.2 Greenness

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 at the Census tract level, using a Poisson distribution

f <- area_esp_vert_2011ct ~ wSCOREMAT.2011.Q + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2011ct ~ wSCOREMAT.2011.Q + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx, 
                 family = Poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2011ct ~ wSCOREMAT.2011.Q + offset(log(ct_area_hct)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                  Estimate Cond. SE t-value p-value
## (Intercept)      -0.59856  0.04009 -14.931       0
## wSCOREMAT.2011.Q -0.09327  0.01094  -8.527       0
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##    1.rho 
## 0.138379 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.05515  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2410.162

ci.lmm <- confint(res.lmm, 'wSCOREMAT.2011.Q')

## lower wSCOREMAT.2011.Q upper wSCOREMAT.2011.Q 
##            -0.11472563            -0.07177056

# Testing main effect
res.lmm.0 <- update(res.lmm, . ~ . - wSCOREMAT.2011.Q)
LRT(res.lmm.0, res.lmm)

##      chi2_LR df      p_value
## p_v 68.11096  1 1.110223e-16

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

Interpretation of the wSCOREMAT.2011.Q coefficient (significant): we have \(e^{-0.093}\) = 0.911 (95%CI: 0.892 – 0.931), which means each increase of 1 quintile in the Material Score leads to a 8.9% decrease in the percentage of greenspace area within CT in 2011.

4.1.3 Canopy (trees)

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 at the Census tract level, using a Poisson distribution

f <- area_esp_vert_high_2011ct ~ wSCOREMAT.2011.Q + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2011ct ~ wSCOREMAT.2011.Q + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx, 
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2011ct ~ wSCOREMAT.2011.Q + offset(log(ct_area_hct)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                  Estimate Cond. SE t-value   p-value
## (Intercept)       -1.2846  0.06041  -21.27 0.000e+00
## wSCOREMAT.2011.Q  -0.1294  0.01655   -7.82 5.329e-15
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1376847 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.1306  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2154.052

ci.lmm <- confint(res.lmm, 'wSCOREMAT.2011.Q')

## lower wSCOREMAT.2011.Q upper wSCOREMAT.2011.Q 
##             -0.1619265             -0.0968720

# Testing main effect
res.lmm.0 <- update(res.lmm, . ~ . - wSCOREMAT.2011.Q)
LRT(res.lmm.0, res.lmm)

##     chi2_LR df      p_value
## p_v 58.1149  1 2.475797e-14

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

Interpretation of the vis_minority_2011.Q coefficient (significant): we have \(e^{NA}\) = NA (95%CI: 0.851 – 0.908), which means each increase of 1 quintile in the Material Score leads to a 12.1% decrease in the percentage of tree canopy area within CT in 2011.

4.2 UC vs Visible minority

4.2.1 Bike lane length (hurdle)

Bike lane ratio to streets (in %) at the Census tract level

f <- Bike_lane_total.hm.2011ct ~ vis_minority_2011.Q + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

# Zero model
res.lmm.zero <- fitme(I(Bike_lane_total.hm.2011ct != 0) ~ vis_minority_2011.Q + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.zero, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2011ct != 0) ~ vis_minority_2011.Q + offset(log(street_length.hm)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                     Estimate Cond. SE t-value   p-value
## (Intercept)           -2.536  0.33404  -7.592 3.153e-14
## vis_minority_2011.Q   -0.212  0.08987  -2.359 1.834e-02
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1377585 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  1.356  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -354.9056

ci.lmm.0 <- confint(res.lmm.zero, 'vis_minority_2011.Q')

## lower vis_minority_2011.Q upper vis_minority_2011.Q 
##               -0.40490772               -0.02914871

res.lmm.0 <- update(res.lmm.zero, . ~ . - vis_minority_2011.Q)
LRT(res.lmm.0, res.lmm.zero)

##      chi2_LR df    p_value
## p_v 5.144237  1 0.02332365

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.zero, plot = F)
  plot(simout, title = "DHARMa residual | Logit")
}

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2011ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2011ct ~ vis_minority_2011.Q + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2011ct ~ vis_minority_2011.Q + offset(log(street_length.hm)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                     Estimate Cond. SE t-value p-value
## (Intercept)         -2.03046  0.09576 -21.204 0.00000
## vis_minority_2011.Q -0.06903  0.02867  -2.408 0.01605
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1297798 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.3876  
## # of obs: 469; # of groups: ct_no, 469 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1730.437

ci.lmm.cnt <- confint(res.lmm.cnt, 'vis_minority_2011.Q')

## lower vis_minority_2011.Q upper vis_minority_2011.Q 
##               -0.12556369               -0.01248152

res.lmm.0 <- update(res.lmm.cnt, . ~ . - vis_minority_2011.Q)
LRT(res.lmm.0, res.lmm.cnt)

##      chi2_LR df    p_value
## p_v 5.704475  1 0.01692172

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.cnt, plot = F)
  plot(simout, title = "DHARMa residual | Count (truncated Poisson)")
}

# AIC
AIC(res.lmm.zero)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.zero$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4178.686

Interpretation of the vis_minority_2011.Q coefficient: - model zero-hurdle (non significant): we have \(e^{-0.212}\) = 0.809 (95%CI: 0.667 – 0.971), which means each increase of 1 quintile in the proportion of visible minority 2011 leads to a NA% decrease the chance of having a bicycle lane in the CT - model count: we have \(e^{-0.069}\) = 0.933 (95%CI: 0.882 – 0.988), which means in CTs with bike lanes, each increase of 1 quintile in the Material Score 2011 leads to a 6.7% decrease the ratio of bike lanes to street in 2011.

4.2.2 Greenness

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_2011ct ~ vis_minority_2011.Q + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2011ct ~ vis_minority_2011.Q + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx, 
                 family = Poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2011ct ~ vis_minority_2011.Q + offset(log(ct_area_hct)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                     Estimate Cond. SE t-value  p-value
## (Intercept)         -0.68172  0.04080 -16.711 0.00e+00
## vis_minority_2011.Q -0.06827  0.01151  -5.931 3.02e-09
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1385835 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.05926  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2421.774

ci.lmm <- confint(res.lmm, 'vis_minority_2011.Q')

## lower vis_minority_2011.Q upper vis_minority_2011.Q 
##               -0.09084917               -0.04560224

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

Interpretation of the vis_minority_2011.Q coefficient (significant): we have \(e^{-0.068}\) = 0.934 (95%CI: 0.913 – 0.955), which means each increase of 1 quintile in the proportion of visible minority leads to a 6.6% decrease in the percentage of greenspace area within CT in 2011.

4.2.3 Canopy (trees)

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_high_2011ct ~ vis_minority_2011.Q + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2011ct ~ vis_minority_2011.Q + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx, 
                 family = Poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2011ct ~ vis_minority_2011.Q + offset(log(ct_area_hct)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                     Estimate Cond. SE t-value   p-value
## (Intercept)          -1.3612  0.06080  -22.39 0.000e+00
## vis_minority_2011.Q  -0.1094  0.01722   -6.35 2.152e-10
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1380368 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.1366  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2159.726

ci.lmm <- confint(res.lmm, 'vis_minority_2011.Q')

## lower vis_minority_2011.Q upper vis_minority_2011.Q 
##               -0.14321003               -0.07552651

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

Interpretation of the vis_minority_2011.Q coefficient (significant): we have \(e^{-0.109}\) = 0.896 (95%CI: 0.867 – 0.927), which means each increase of 1 quintile in the proportion of visible minority leads to a 10.4% decrease in the percentage of tree canopy area within CT in 2011.

4.3 UC vs gentrified CT

Gentrified CT between 2011 and 2016

4.3.1 Bike lane length (hurdle)

Bike lane ratio to streets (in %) at the Census tract level

f <- Bike_lane_total.hm.2011ct ~ gentrified_2016_2011 + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

# Zero model
res.lmm.zero <- fitme(I(Bike_lane_total.hm.2011ct != 0) ~ gentrified_2016_2011 + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.zero, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2011ct != 0) ~ gentrified_2016_2011 + offset(log(street_length.hm)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                          Estimate Cond. SE t-value p-value
## (Intercept)              -3.12397   0.1952 -16.003  0.0000
## gentrified_2016_2011TRUE -0.06627   0.2473  -0.268  0.7887
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1378747 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  1.496  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -357.4465

ci.lmm.0 <- confint(res.lmm.zero, 'gentrified_2016_2011TRUE')

## lower gentrified_2016_2011TRUE upper gentrified_2016_2011TRUE 
##                     -0.6062718                      0.4522833

res.lmm.0 <- update(res.lmm.zero, . ~ . - gentrified_2016_2011)
LRT(res.lmm.0, res.lmm.zero)

##        chi2_LR df   p_value
## p_v 0.06253228  1 0.8025374

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.zero, plot = F)
  plot(simout, title = "DHARMa residual | Logit")
}

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2011ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2011ct ~ gentrified_2016_2011 + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2011ct ~ gentrified_2016_2011 + offset(log(street_length.hm)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                          Estimate Cond. SE t-value p-value
## (Intercept)              -2.26118  0.05223 -43.290  0.0000
## gentrified_2016_2011TRUE  0.09494  0.08002   1.186  0.2355
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1267498 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.3946  
## # of obs: 469; # of groups: ct_no, 469 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1732.647

ci.lmm.cnt <- confint(res.lmm.cnt, 'gentrified_2016_2011TRUE')

## lower gentrified_2016_2011TRUE upper gentrified_2016_2011TRUE 
##                    -0.06921123                     0.25966646

res.lmm.0 <- update(res.lmm.cnt, . ~ . - gentrified_2016_2011)
LRT(res.lmm.0, res.lmm.cnt)

##      chi2_LR df   p_value
## p_v 1.285916  1 0.2568019

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.cnt, plot = F)
  plot(simout, title = "DHARMa residual | Count (truncated Poisson)")
}

# AIC
AIC(res.lmm.zero)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.zero$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4188.186

Interpretation of the gentrified_2016_2011 coefficient: none significant - model zero-hurdle (non significant): we have \(e^{-0.066}\) = 0.936 (95%CI: 0.545 – 1.572) - model count: we have \(e^{0.095}\) = 1.1 (95%CI: 0.933 – 1.296)

4.3.2 Greenness

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_2011ct ~ gentrified_2016_2011 + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2011ct ~ gentrified_2016_2011 + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx, 
                 family = Poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2011ct ~ gentrified_2016_2011 + offset(log(ct_area_hct)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                          Estimate Cond. SE t-value   p-value
## (Intercept)               -0.8304  0.02578 -32.205 0.000e+00
## gentrified_2016_2011TRUE  -0.1964  0.03343  -5.875 4.234e-09
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1385641 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.05997  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2421.862

ci.lmm <- confint(res.lmm, 'gentrified_2016_2011TRUE')

## lower gentrified_2016_2011TRUE upper gentrified_2016_2011TRUE 
##                     -0.2620145                     -0.1306189

# Testing main effect
res.lmm.0 <- update(res.lmm, . ~ . - gentrified_2016_2011)
LRT(res.lmm.0, res.lmm)

##      chi2_LR df      p_value
## p_v 33.56416  1 6.895166e-09

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

Interpretation of the gentrified_2016_2011 coefficient (significant): we have \(e^{-0.196}\) = 0.822 (95%CI: 0.769 – 0.878), which means gentrified CTs exhibit a 17.8% decrease in the percentage of greenspace area within CT in 2011.

4.3.3 Canopy (trees)

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_high_2011ct ~ gentrified_2016_2011 + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2011ct ~ gentrified_2016_2011 + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx, 
                 family = Poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2011ct ~ gentrified_2016_2011 + offset(log(ct_area_hct)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                          Estimate Cond. SE t-value  p-value
## (Intercept)               -1.6372  0.03951 -41.442 0.000000
## gentrified_2016_2011TRUE  -0.1505  0.04990  -3.015 0.002568
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1380114 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.1457  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2174.734

ci.lmm <- confint(res.lmm, 'gentrified_2016_2011TRUE')

## lower gentrified_2016_2011TRUE upper gentrified_2016_2011TRUE 
##                    -0.24862544                    -0.05240792

# Testing main effect
res.lmm.0 <- update(res.lmm, . ~ . - gentrified_2016_2011)
LRT(res.lmm.0, res.lmm)

##      chi2_LR df     p_value
## p_v 9.025009  1 0.002663107

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

Interpretation of the gentrified_2016_2011 coefficient (significant): we have \(e^{-0.15}\) = 0.86 (95%CI: 0.78 – 0.949), which means gentrified CTs exhibit a 14% decrease in the percentage of tree canopy area within CT in 2011

5 Association between SES and UC in 2011 | SES as categories

UPDATE 2022-08-18: adding the same models, with discrete SES variables

5.1 UC vs Pampalon | material

5.1.1 Bike lane length (hurdle)

f <- Bike_lane_total.hm.2011ct ~ factor(wSCOREMAT.2011.Q) + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

# Zero model
res.lmm.zero <- fitme(I(Bike_lane_total.hm.2011ct != 0) ~ factor(wSCOREMAT.2011.Q) + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.zero, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2011ct != 0) ~ factor(wSCOREMAT.2011.Q) + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                           Estimate Cond. SE t-value   p-value
## (Intercept)                -2.6782   0.3458 -7.7452 9.548e-15
## factor(wSCOREMAT.2011.Q)2  -0.4105   0.3926 -1.0455 2.958e-01
## factor(wSCOREMAT.2011.Q)3  -0.1724   0.4091 -0.4215 6.734e-01
## factor(wSCOREMAT.2011.Q)4  -0.3350   0.4134 -0.8105 4.176e-01
## factor(wSCOREMAT.2011.Q)5  -1.1552   0.4092 -2.8232 4.754e-03
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1376613 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  1.49  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -352.3199

res.lmm.0 <- update(res.lmm.zero, . ~ . -factor(wSCOREMAT.2011.Q))
LRT(res.lmm.0, res.lmm.zero)

##      chi2_LR df    p_value
## p_v 10.06913  4 0.03927914

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.zero, plot = F)
  plot(simout, title = "DHARMa residual | Logit")
}

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2011ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2011ct ~ factor(wSCOREMAT.2011.Q) + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2011ct ~ factor(wSCOREMAT.2011.Q) + offset(log(street_length.hm)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                           Estimate Cond. SE t-value  p-value
## (Intercept)                -2.0448  0.08497 -24.064 0.000000
## factor(wSCOREMAT.2011.Q)2  -0.1713  0.10504  -1.631 0.102979
## factor(wSCOREMAT.2011.Q)3  -0.2997  0.10741  -2.790 0.005265
## factor(wSCOREMAT.2011.Q)4  -0.1538  0.11014  -1.397 0.162501
## factor(wSCOREMAT.2011.Q)5  -0.3097  0.12349  -2.508 0.012140
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1315181 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.3866  
## # of obs: 469; # of groups: ct_no, 469 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1733.093

res.lmm.0 <- update(res.lmm.cnt, . ~ . -factor(wSCOREMAT.2011.Q))
LRT(res.lmm.0, res.lmm.cnt)

##      chi2_LR df    p_value
## p_v 9.933888  4 0.04155618

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.cnt, plot = F)
  plot(simout, title = "DHARMa residual | Count (truncated Poisson)")
}

# AIC
AIC(res.lmm.zero)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.zero$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4184.826

Transforming the wSCOREMAT.2011.Q coefficients (discrete):

# Zero model
round(exp(res.lmm.zero[["fixef"]]), 3) %>%
  knitr::kable(caption="Zero model transformed coeffs")

Zero model transformed coeffs

	x
(Intercept)	0.069
factor(wSCOREMAT.2011.Q)2	0.663
factor(wSCOREMAT.2011.Q)3	0.842
factor(wSCOREMAT.2011.Q)4	0.715
factor(wSCOREMAT.2011.Q)5	0.315

# Count model
round(exp(res.lmm.cnt[["fixef"]]), 3) %>%
  knitr::kable(caption="Count model transformed coeffs")

Count model transformed coeffs

	x
(Intercept)	0.129
factor(wSCOREMAT.2011.Q)2	0.843
factor(wSCOREMAT.2011.Q)3	0.741
factor(wSCOREMAT.2011.Q)4	0.857
factor(wSCOREMAT.2011.Q)5	0.734

5.1.2 Greenness

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 at the Census tract level, using a Poisson distribution

f <- area_esp_vert_2011ct ~ factor(wSCOREMAT.2011.Q) + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2011ct ~ factor(wSCOREMAT.2011.Q) + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx, 
                 family = Poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2011ct ~ factor(wSCOREMAT.2011.Q) + offset(log(ct_area_hct)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                           Estimate Cond. SE t-value   p-value
## (Intercept)               -0.71469  0.03647 -19.594 0.000e+00
## factor(wSCOREMAT.2011.Q)2 -0.08137  0.03997  -2.036 4.176e-02
## factor(wSCOREMAT.2011.Q)3 -0.12132  0.04238  -2.863 4.201e-03
## factor(wSCOREMAT.2011.Q)4 -0.22252  0.04335  -5.133 2.850e-07
## factor(wSCOREMAT.2011.Q)5 -0.40739  0.04796  -8.494 0.000e+00
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1383781 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.05402  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2406.448

# Testing main effect
res.lmm.0 <- update(res.lmm, . ~ . - factor(wSCOREMAT.2011.Q))
LRT(res.lmm.0, res.lmm)

##     chi2_LR df      p_value
## p_v 75.5386  4 1.554312e-15

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

Transforming the wSCOREMAT.2011.Q coefficients (discrete):

# Zero model
round(exp(res.lmm[["fixef"]]), 3) %>%
  knitr::kable(caption="Transformed coeffs")

Transformed coeffs

	x
(Intercept)	0.489
factor(wSCOREMAT.2011.Q)2	0.922
factor(wSCOREMAT.2011.Q)3	0.886
factor(wSCOREMAT.2011.Q)4	0.801
factor(wSCOREMAT.2011.Q)5	0.665

5.1.3 Canopy (trees)

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 at the Census tract level, using a Poisson distribution

f <- area_esp_vert_high_2011ct ~ factor(wSCOREMAT.2011.Q) + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2011ct ~ factor(wSCOREMAT.2011.Q) + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx, 
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2011ct ~ factor(wSCOREMAT.2011.Q) + offset(log(ct_area_hct)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                           Estimate Cond. SE t-value   p-value
## (Intercept)                -1.4370  0.05487 -26.188 0.000e+00
## factor(wSCOREMAT.2011.Q)2  -0.1328  0.06019  -2.207 2.732e-02
## factor(wSCOREMAT.2011.Q)3  -0.1644  0.06378  -2.578 9.934e-03
## factor(wSCOREMAT.2011.Q)4  -0.3365  0.06576  -5.116 3.113e-07
## factor(wSCOREMAT.2011.Q)5  -0.5602  0.07293  -7.682 1.565e-14
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1377046 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.1292  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2151.268

# Testing main effect
res.lmm.0 <- update(res.lmm, . ~ . - factor(wSCOREMAT.2011.Q))
LRT(res.lmm.0, res.lmm)

##      chi2_LR df      p_value
## p_v 63.68247  4 4.874989e-13

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

Transforming the wSCOREMAT.2011.Q coefficients (discrete):

# Zero model
round(exp(res.lmm[["fixef"]]), 3) %>%
  knitr::kable(caption="Transformed coeffs")

Transformed coeffs

	x
(Intercept)	0.238
factor(wSCOREMAT.2011.Q)2	0.876
factor(wSCOREMAT.2011.Q)3	0.848
factor(wSCOREMAT.2011.Q)4	0.714
factor(wSCOREMAT.2011.Q)5	0.571

5.2 UC vs Visible minority

5.2.1 Bike lane length (hurdle)

Bike lane ratio to streets (in %) at the Census tract level

f <- Bike_lane_total.hm.2011ct ~ factor(vis_minority_2011.Q) + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

# Zero model
res.lmm.zero <- fitme(I(Bike_lane_total.hm.2011ct != 0) ~ factor(vis_minority_2011.Q) + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.zero, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2011ct != 0) ~ factor(vis_minority_2011.Q) + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                              Estimate Cond. SE   t-value p-value
## (Intercept)                  -2.96762   0.3115 -9.526787 0.00000
## factor(vis_minority_2011.Q)2  0.24833   0.3889  0.638526 0.52313
## factor(vis_minority_2011.Q)3 -0.30809   0.3714 -0.829465 0.40684
## factor(vis_minority_2011.Q)4  0.00379   0.3925  0.009655 0.99230
## factor(vis_minority_2011.Q)5 -0.90644   0.3872 -2.340770 0.01924
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1376616 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  1.41  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -352.3024

res.lmm.0 <- update(res.lmm.zero, . ~ . - factor(vis_minority_2011.Q))
LRT(res.lmm.0, res.lmm.zero)

##      chi2_LR df    p_value
## p_v 10.35059  4 0.03491857

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.zero, plot = F)
  plot(simout, title = "DHARMa residual | Logit")
}

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2011ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2011ct ~ factor(vis_minority_2011.Q) + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2011ct ~ factor(vis_minority_2011.Q) + offset(log(street_length.hm)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                              Estimate Cond. SE t-value p-value
## (Intercept)                  -2.13756  0.08458 -25.274 0.00000
## factor(vis_minority_2011.Q)2  0.06116  0.10160   0.602 0.54720
## factor(vis_minority_2011.Q)3 -0.15828  0.10811  -1.464 0.14317
## factor(vis_minority_2011.Q)4 -0.19282  0.11075  -1.741 0.08168
## factor(vis_minority_2011.Q)5 -0.20731  0.12665  -1.637 0.10165
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1300438 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.3847  
## # of obs: 469; # of groups: ct_no, 469 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1728.974

res.lmm.0 <- update(res.lmm.cnt, . ~ . - factor(vis_minority_2011.Q))
LRT(res.lmm.0, res.lmm.cnt)

##      chi2_LR df    p_value
## p_v 8.631541  4 0.07099879

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.cnt, plot = F)
  plot(simout, title = "DHARMa residual | Count (truncated Poisson)")
}

# AIC
AIC(res.lmm.zero)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.zero$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4176.552

Transforming the wSCOREMAT.2011.Q coefficients (discrete):

# Zero model
round(exp(res.lmm.zero[["fixef"]]), 3) %>%
  knitr::kable(caption="Zero model transformed coeffs")

Zero model transformed coeffs

	x
(Intercept)	0.051
factor(vis_minority_2011.Q)2	1.282
factor(vis_minority_2011.Q)3	0.735
factor(vis_minority_2011.Q)4	1.004
factor(vis_minority_2011.Q)5	0.404

# Count model
round(exp(res.lmm.cnt[["fixef"]]), 3) %>%
  knitr::kable(caption="Count model transformed coeffs")

Count model transformed coeffs

	x
(Intercept)	0.118
factor(vis_minority_2011.Q)2	1.063
factor(vis_minority_2011.Q)3	0.854
factor(vis_minority_2011.Q)4	0.825
factor(vis_minority_2011.Q)5	0.813

5.2.2 Greenness

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_2011ct ~ factor(vis_minority_2011.Q) + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2011ct ~ factor(vis_minority_2011.Q) + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx, 
                 family = Poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2011ct ~ factor(vis_minority_2011.Q) + offset(log(ct_area_hct)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                              Estimate Cond. SE t-value   p-value
## (Intercept)                  -0.76472  0.03621 -21.118 0.000e+00
## factor(vis_minority_2011.Q)2 -0.05421  0.04138  -1.310 1.902e-01
## factor(vis_minority_2011.Q)3 -0.10559  0.04297  -2.457 1.401e-02
## factor(vis_minority_2011.Q)4 -0.14248  0.04466  -3.190 1.423e-03
## factor(vis_minority_2011.Q)5 -0.30573  0.04934  -6.196 5.793e-10
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1385852 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.05874  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2418.952

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

Transforming the wSCOREMAT.2011.Q coefficients (discrete):

# Zero model
round(exp(res.lmm[["fixef"]]), 3) %>%
  knitr::kable(caption="Transformed coeffs")

Transformed coeffs

	x
(Intercept)	0.465
factor(vis_minority_2011.Q)2	0.947
factor(vis_minority_2011.Q)3	0.900
factor(vis_minority_2011.Q)4	0.867
factor(vis_minority_2011.Q)5	0.737

5.2.3 Canopy (trees)

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_high_2011ct ~ factor(vis_minority_2011.Q) + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2011ct ~ factor(vis_minority_2011.Q) + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx, 
                 family = Poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2011ct ~ factor(vis_minority_2011.Q) + offset(log(ct_area_hct)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                              Estimate Cond. SE t-value   p-value
## (Intercept)                  -1.48392  0.05407 -27.443 0.000e+00
## factor(vis_minority_2011.Q)2 -0.09687  0.06175  -1.569 1.167e-01
## factor(vis_minority_2011.Q)3 -0.17639  0.06414  -2.750 5.961e-03
## factor(vis_minority_2011.Q)4 -0.29448  0.06714  -4.386 1.154e-05
## factor(vis_minority_2011.Q)5 -0.45506  0.07409  -6.142 8.157e-10
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1380636 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.1366  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2159.165

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

Transforming the wSCOREMAT.2011.Q coefficients (discrete):

# Zero model
round(exp(res.lmm[["fixef"]]), 3) %>%
  knitr::kable(caption="Transformed coeffs")

Transformed coeffs

	x
(Intercept)	0.227
factor(vis_minority_2011.Q)2	0.908
factor(vis_minority_2011.Q)3	0.838
factor(vis_minority_2011.Q)4	0.745
factor(vis_minority_2011.Q)5	0.634

5.3 UC vs gentrified CT

No new models here, as gentrified variable is already used as a pure categorical variable.

6 Association between SES and Urban Interventions (2011 to 2016)

Looking at objective #1 | do urban interventions tend to be located in low SES neighborhoods?. We look at \[Urban Intervention_{2011 \to 2016} = f(SES_{2011})\] as well as \[Urban Intervention_{2011 \to 2016} = f(Gentrification_{2011 \to 2016})\]

Here \(Urban Intervention\) means the changes in the urban environment features, such as variation of bike lane length, greenness coverage, etc.

Apparently, change in rates are rather modeled as a pre-post model, as suggested in Jones’s answer. Hence, we model change in interventions between 2011 and 2016 as \[UC_{2016} = \beta_{0} + \beta_{1} * UC_{2011} + \beta_{2} * SES\]

Mostly redundant with multi-level approach below.

6.1 UI vs Pampalon | material

6.1.1 Bike lane length change (hurdle)

Bike lane length change

f <- Bike_lane_total.hm.2016ct ~ wSCOREMAT.2011.Q * Bike_lane.by.street.2011ct + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm.0 <- fitme(I(Bike_lane_total.hm.2016ct != 0) ~ wSCOREMAT.2011.Q * Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.0, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2016ct != 0) ~ wSCOREMAT.2011.Q * Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                                             Estimate Cond. SE t-value   p-value
## (Intercept)                                 -5.12247   0.8914 -5.7468 9.094e-09
## wSCOREMAT.2011.Q                             0.05264   0.2153  0.2445 8.069e-01
## Bike_lane.by.street.2011ct                   3.93126   2.5484  1.5426 1.229e-01
## wSCOREMAT.2011.Q:Bike_lane.by.street.2011ct -0.39374   0.5959 -0.6607 5.088e-01
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1377292 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  5.737  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -149.3657

# NB: not converging | but not needed, use Wald p-value instead or LRT
# ci.lmm.0.1 <- confint(res.lmm.0, "wSCOREMAT.2011.Q")
# ci.lmm.0.2 <- confint(res.lmm.0, "Bike_lane.by.street.2011ct")
# ci.lmm.0.3 <- confint(res.lmm.0, "wSCOREMAT.2011.Q:Bike_lane.by.street.2011ct")

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.0, plot = F)
  plot(simout)
}

# Plotting interaction || MEANINGLESS
# .t <- clean_bei$df
# .t["predict"] <- as.vector(predict(res.lmm.0))
# 
# ggplot(.t, aes(y=predict, x=Bike_lane.by.street.2011ct, colour=factor(wSCOREMAT.2011.Q), fill=factor(wSCOREMAT.2011.Q))) + 
#   geom_smooth(method = "lm", alpha=.1) +
#   geom_point() + 
#   labs(colour='wSCOREMAT.2011.Q', fill='wSCOREMAT.2011.Q')

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2016ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2016ct ~ wSCOREMAT.2011.Q * Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2016ct ~ wSCOREMAT.2011.Q * Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                               Estimate Cond. SE   t-value
## (Intercept)                                 -2.6735086 0.085129 -31.40532
## wSCOREMAT.2011.Q                            -0.0084696 0.023916  -0.35414
## Bike_lane.by.street.2011ct                   0.0537190 0.004433  12.11790
## wSCOREMAT.2011.Q:Bike_lane.by.street.2011ct  0.0001078 0.001406   0.07667
##                                             p-value
## (Intercept)                                  0.0000
## wSCOREMAT.2011.Q                             0.7232
## Bike_lane.by.street.2011ct                   0.0000
## wSCOREMAT.2011.Q:Bike_lane.by.street.2011ct  0.9389
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1502892 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.1125  
## # of obs: 564; # of groups: ct_no, 564 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1884.428

# ci.lmm.cnt.1 <- confint(res.lmm.cnt, "wSCOREMAT.2011.Q")
# ci.lmm.cnt.2 <- confint(res.lmm.cnt, "Bike_lane.by.street.2011ct")
# ci.lmm.cnt.3 <- confint(res.lmm.cnt, "wSCOREMAT.2011.Q:Bike_lane.by.street.2011ct")

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.cnt, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei.cnt$df
.t["predict"] <- as.vector(predict(res.lmm.cnt))

g_mat_bk.hrdl <- ggplot(.t, aes(y=100*predict/street_length.hm, x=Bike_lane.by.street.2011ct, colour=factor(wSCOREMAT.2011.Q), fill=factor(wSCOREMAT.2011.Q))) + 
  geom_smooth(method = "lm", alpha=.1, linetype="dashed") +
  labs(colour='wSCOREMAT.2011.Q', fill='wSCOREMAT.2011.Q')
g_mat_bk.hrdl

# AIC
AIC(res.lmm.0)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.0$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4079.588

Interpretation of the wSCOREMAT.2011.Q coefficient | Zero model (not significant): we have \(e^{0.053}\) = 1.054 Interpretation of the wSCOREMAT.2011.Q coefficient | Count model (not significant): we have \(e^{-0.008}\) = 0.992

Coefficient interpretation (marginal + interaction) as relative risk.

6.1.2 Greenness change

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_2017ct ~ wSCOREMAT.2011.Q * pct_esp_vert_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2017ct ~ wSCOREMAT.2011.Q*pct_esp_vert_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2017ct ~ wSCOREMAT.2011.Q * pct_esp_vert_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                       Estimate  Cond. SE t-value   p-value
## (Intercept)                          -1.449918 0.0493086 -29.405 0.000e+00
## wSCOREMAT.2011.Q                     -0.061732 0.0149037  -4.142 3.442e-05
## pct_esp_vert_2011ct                   0.015957 0.0008800  18.132 0.000e+00
## wSCOREMAT.2011.Q:pct_esp_vert_2011ct  0.001138 0.0003134   3.633 2.804e-04
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1364178 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.004538  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2010.108

ci.lmm.1 <- confint(res.lmm, "wSCOREMAT.2011.Q")

## lower wSCOREMAT.2011.Q upper wSCOREMAT.2011.Q 
##            -0.09102817            -0.03232795

ci.lmm.2 <- confint(res.lmm, "pct_esp_vert_2011ct")

## lower pct_esp_vert_2011ct upper pct_esp_vert_2011ct 
##                0.01421609                0.01772789

ci.lmm.3 <- confint(res.lmm, "wSCOREMAT.2011.Q:pct_esp_vert_2011ct")

## lower wSCOREMAT.2011.Q:pct_esp_vert_2011ct 
##                               0.0005235603 
## upper wSCOREMAT.2011.Q:pct_esp_vert_2011ct 
##                               0.0017542437

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei$df
.t["predict"] <- as.vector(predict(res.lmm))

g_mat_gr <- ggplot(.t, aes(y=100*predict/ct_area_hct, x=pct_esp_vert_2011ct, colour=factor(wSCOREMAT.2011.Q), fill=factor(wSCOREMAT.2011.Q))) + 
  geom_smooth(method = "lm", alpha=.1) +
  labs(colour='wSCOREMAT.2011.Q', fill='wSCOREMAT.2011.Q')
g_mat_gr

Interpretation of the wSCOREMAT.2011.Q coefficient (significant): we have \(e^{-0.062}\) = 0.94 (95%CI: 0.913 – 0.968)

Coefficient interpretation (marginal + interaction) as relative risk.

# Compute combined effects (marginal + interaction) for each quintile of SES:
i_e <- data.frame(wSCOREMAT.2011.Q=c(1,3,5))
i_e["UC2011.effect"] <- res.lmm[["fixef"]]['pct_esp_vert_2011ct'] + i_e["wSCOREMAT.2011.Q"] * res.lmm[["fixef"]]['wSCOREMAT.2011.Q:pct_esp_vert_2011ct']
i_e["UC2011.relative.risk"] <- exp(i_e["UC2011.effect"])
i_e

# Compute combined effects (marginal + interaction) for each quintile of SES:
i_e <- data.frame(pct_esp_vert_2011ct = quantile(clean_bei$df$pct_esp_vert_2011ct)[2:4])
i_e["SES.effect"] <- res.lmm[["fixef"]]['wSCOREMAT.2011.Q'] + i_e["pct_esp_vert_2011ct"] * res.lmm[["fixef"]]['wSCOREMAT.2011.Q:pct_esp_vert_2011ct']
i_e["SES.relative.risk"] <- exp(i_e["SES.effect"])
i_e

6.1.3 Canopy (trees) change

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_high_2017ct ~ wSCOREMAT.2011.Q * pct_esp_vert_high_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2017ct ~ wSCOREMAT.2011.Q * pct_esp_vert_high_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2017ct ~ wSCOREMAT.2011.Q * pct_esp_vert_high_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                            Estimate  Cond. SE t-value   p-value
## (Intercept)                               -2.085884 0.0497948 -41.890 0.000e+00
## wSCOREMAT.2011.Q                          -0.119070 0.0160742  -7.408 1.287e-13
## pct_esp_vert_high_2011ct                   0.028240 0.0016388  17.232 0.000e+00
## wSCOREMAT.2011.Q:pct_esp_vert_high_2011ct  0.005592 0.0006923   8.077 6.661e-16
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1379013 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.0105  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                        logLik
## p_v(h) (marginal L): -1791.84

ci.lmm.1 <- confint(res.lmm, "wSCOREMAT.2011.Q")

## lower wSCOREMAT.2011.Q upper wSCOREMAT.2011.Q 
##            -0.15066242            -0.08758274

ci.lmm.2 <- confint(res.lmm, "pct_esp_vert_high_2011ct")

## lower pct_esp_vert_high_2011ct upper pct_esp_vert_high_2011ct 
##                     0.02502735                     0.03147717

ci.lmm.3 <- confint(res.lmm, "wSCOREMAT.2011.Q:pct_esp_vert_high_2011ct")

## lower wSCOREMAT.2011.Q:pct_esp_vert_high_2011ct 
##                                     0.004235836 
## upper wSCOREMAT.2011.Q:pct_esp_vert_high_2011ct 
##                                     0.006962135

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei$df
.t["predict"] <- as.vector(predict(res.lmm))

g_mat_tc <- ggplot(.t, aes(y=100*predict/ct_area_hct, x=pct_esp_vert_high_2011ct, colour=factor(wSCOREMAT.2011.Q), fill=factor(wSCOREMAT.2011.Q))) + 
  geom_smooth(method = "lm", alpha=.1) +
  labs(colour='wSCOREMAT.2011.Q', fill='wSCOREMAT.2011.Q')
g_mat_tc

Interpretation of the wSCOREMAT.2011.Q coefficient (significant): we have \(e^{-0.119}\) = 0.888 (95%CI: 0.86 – 0.916)

Coefficient interpretation (marginal + interaction) as relative risk.

# Compute combined effects (marginal + interaction) for each quintile of SES:
i_e <- data.frame(wSCOREMAT.2011.Q=c(1,3,5))
i_e["UC2011.effect"] <- res.lmm[["fixef"]]['pct_esp_vert_high_2011ct'] + i_e["wSCOREMAT.2011.Q"] * res.lmm[["fixef"]]['wSCOREMAT.2011.Q:pct_esp_vert_high_2011ct']
i_e["UC2011.relative.risk"] <- exp(i_e["UC2011.effect"])
i_e

# Compute combined effects (marginal + interaction) for each quintile of SES:
i_e <- data.frame(pct_esp_vert_high_2011ct = quantile(clean_bei$df$pct_esp_vert_high_2011ct)[2:4])
i_e["SES.effect"] <- res.lmm[["fixef"]]['wSCOREMAT.2011.Q'] + i_e["pct_esp_vert_high_2011ct"] * res.lmm[["fixef"]]['wSCOREMAT.2011.Q:pct_esp_vert_high_2011ct']
i_e["SES.relative.risk"] <- exp(i_e["SES.effect"])
i_e

6.2 UI vs Visible minority

6.2.1 Bike lane length change (hurdle)

Bike lane length change

f <- Bike_lane_total.hm.2016ct ~ vis_minority_2011.Q * Bike_lane.by.street.2011ct + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm.zero <- fitme(I(Bike_lane_total.hm.2016ct != 0) ~ vis_minority_2011.Q * Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.zero, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2016ct != 0) ~ vis_minority_2011.Q * Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                                                Estimate Cond. SE t-value
## (Intercept)                                     -3.2206   0.9043 -3.5614
## vis_minority_2011.Q                             -0.4739   0.2291 -2.0684
## Bike_lane.by.street.2011ct                       4.9368   4.1706  1.1837
## vis_minority_2011.Q:Bike_lane.by.street.2011ct  -0.5239   0.9395 -0.5576
##                                                  p-value
## (Intercept)                                    0.0003689
## vis_minority_2011.Q                            0.0386031
## Bike_lane.by.street.2011ct                     0.2365265
## vis_minority_2011.Q:Bike_lane.by.street.2011ct 0.5770925
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1379043 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  6.547  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -145.4209

# p-value not far from 0.05, use LRT to refine test
res.lmm.0 <- update(res.lmm.zero, . ~ . - vis_minority_2011.Q)
LRT(res.lmm.0, res.lmm.zero)

##      chi2_LR df    p_value
## p_v 3.522643  1 0.06053585

# NB: not converging
# ci.lmm.0.1 <- confint(res.lmm.0, "vis_minority_2011.Q")
# ci.lmm.0.2 <- confint(res.lmm.0, "Bike_lane.by.street.2011ct")
# ci.lmm.0.3 <- confint(res.lmm.0, "vis_minority_2011.Q:Bike_lane.by.street.2011ct")

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.0, plot = F)
  plot(simout)
}

# Plotting interaction  || MEANINGLESS
# .t <- clean_bei$df
# .t["predict"] <- as.vector(predict(res.lmm.0))
# 
# ggplot(.t, aes(y=100*predict/street_length.hm, x=Bike_lane.by.street.2011ct, colour=factor(vis_minority_2011.Q), fill=factor(vis_minority_2011.Q))) + 
#   geom_smooth(method = "lm", alpha=.1) +
#   labs(colour='vis_minority_2011.Q', fill='vis_minority_2011.Q')

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2016ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2016ct ~ vis_minority_2011.Q * Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2016ct ~ vis_minority_2011.Q * Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                                  Estimate Cond. SE  t-value
## (Intercept)                                    -2.635e+00 0.086877 -30.3275
## vis_minority_2011.Q                            -2.080e-02 0.024749  -0.8404
## Bike_lane.by.street.2011ct                      5.415e-02 0.004618  11.7247
## vis_minority_2011.Q:Bike_lane.by.street.2011ct -2.446e-05 0.001491  -0.0164
##                                                p-value
## (Intercept)                                     0.0000
## vis_minority_2011.Q                             0.4007
## Bike_lane.by.street.2011ct                      0.0000
## vis_minority_2011.Q:Bike_lane.by.street.2011ct  0.9869
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##    1.rho 
## 0.150489 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.1121  
## # of obs: 564; # of groups: ct_no, 564 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1880.959

# ci.lmm.cnt.1 <- confint(res.lmm.cnt, "vis_minority_2011.Q")
# ci.lmm.cnt.2 <- confint(res.lmm.cnt, "Bike_lane.by.street.2011ct")
# ci.lmm.cnt.3 <- confint(res.lmm.cnt, "vis_minority_2011.Q:Bike_lane.by.street.2011ct")

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.cnt, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei.cnt$df
.t["predict"] <- as.vector(predict(res.lmm.cnt))

g_vis_bk.hrdl <- ggplot(.t, aes(y=100*predict/street_length.hm, x=Bike_lane.by.street.2011ct, colour=factor(vis_minority_2011.Q), fill=factor(vis_minority_2011.Q))) + 
  geom_smooth(method = "lm", alpha=.1, linetype = "dashed") +
  labs(colour='vis_minority_2011.Q', fill='vis_minority_2011.Q')
g_vis_bk.hrdl

# AIC
AIC(res.lmm.zero)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.zero$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4064.759

Interpretation of the vis_minority_2011.Q coefficient | Zero model (not significant): we have \(e^{-0.474}\) = 0.623 Interpretation of the wSCOREMAT.2011.Q coefficient | Count model (not significant): we have \(e^{-0.021}\) = 0.979

6.2.2 Greenness change

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_2017ct ~ vis_minority_2011.Q * pct_esp_vert_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2017ct ~ vis_minority_2011.Q * pct_esp_vert_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2017ct ~ vis_minority_2011.Q * pct_esp_vert_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                          Estimate  Cond. SE t-value   p-value
## (Intercept)                             -1.464947 0.0488681 -29.978 0.000e+00
## vis_minority_2011.Q                     -0.058931 0.0147090  -4.006 6.163e-05
## pct_esp_vert_2011ct                      0.016177 0.0008521  18.984 0.000e+00
## vis_minority_2011.Q:pct_esp_vert_2011ct  0.001079 0.0002848   3.788 1.518e-04
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##    1.rho 
## 0.136093 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.004657  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2009.835

ci.lmm.1 <- confint(res.lmm, "vis_minority_2011.Q")

## lower vis_minority_2011.Q upper vis_minority_2011.Q 
##               -0.08777005               -0.02998448

ci.lmm.2 <- confint(res.lmm, "pct_esp_vert_2011ct")

## lower pct_esp_vert_2011ct upper pct_esp_vert_2011ct 
##                0.01449601                0.01788267

ci.lmm.3 <- confint(res.lmm, "vis_minority_2011.Q:pct_esp_vert_2011ct")

## lower vis_minority_2011.Q:pct_esp_vert_2011ct 
##                                  0.0005204252 
## upper vis_minority_2011.Q:pct_esp_vert_2011ct 
##                                  0.0016392402

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei$df
.t["predict"] <- as.vector(predict(res.lmm))

g_vis_gr <- ggplot(.t, aes(y=100*predict/ct_area_hct, x=pct_esp_vert_2011ct, colour=factor(vis_minority_2011.Q), fill=factor(vis_minority_2011.Q))) + 
  geom_smooth(method = "lm", alpha=.1) +
  labs(colour='vis_minority_2011.Q', fill='vis_minority_2011.Q')
g_vis_gr

Interpretation of the vis_minority_2011.Q coefficient (significant): we have \(e^{-0.059}\) = 0.943 (95%CI: 0.916 – 0.97)

Coefficient interpretation (marginal + interaction) as relative risk.

# Compute combined effects (marginal + interaction) for each quintile of SES:
i_e <- data.frame(vis_minority_2011.Q=c(1,3,5))
i_e["UC2011.effect"] <- res.lmm[["fixef"]]['pct_esp_vert_2011ct'] + i_e["vis_minority_2011.Q"] * res.lmm[["fixef"]]['vis_minority_2011.Q:pct_esp_vert_2011ct']
i_e["UC2011.relative.risk"] <- exp(i_e["UC2011.effect"])
i_e

# Compute combined effects (marginal + interaction) for each quintile of SES:
i_e <- data.frame(pct_esp_vert_2011ct = quantile(clean_bei$df$pct_esp_vert_2011ct)[2:4])
i_e["SES.effect"] <- res.lmm[["fixef"]]['vis_minority_2011.Q'] + i_e["pct_esp_vert_2011ct"] * res.lmm[["fixef"]]['vis_minority_2011.Q:pct_esp_vert_2011ct']
i_e["SES.relative.risk"] <- exp(i_e["SES.effect"])
i_e

6.2.3 Canopy (trees) change

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_high_2017ct ~ vis_minority_2011.Q * pct_esp_vert_high_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2017ct ~ vis_minority_2011.Q * pct_esp_vert_high_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2017ct ~ vis_minority_2011.Q * pct_esp_vert_high_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                               Estimate  Cond. SE t-value
## (Intercept)                                  -2.163285 0.0535686 -40.383
## vis_minority_2011.Q                          -0.076677 0.0166197  -4.614
## pct_esp_vert_high_2011ct                      0.031788 0.0017899  17.759
## vis_minority_2011.Q:pct_esp_vert_high_2011ct  0.003336 0.0006397   5.215
##                                                p-value
## (Intercept)                                  0.000e+00
## vis_minority_2011.Q                          3.957e-06
## pct_esp_vert_high_2011ct                     0.000e+00
## vis_minority_2011.Q:pct_esp_vert_high_2011ct 1.842e-07
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1379765 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.01184  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1808.484

ci.lmm.1 <- confint(res.lmm, "vis_minority_2011.Q")

## lower vis_minority_2011.Q upper vis_minority_2011.Q 
##               -0.10934259               -0.04405318

ci.lmm.2 <- confint(res.lmm, "pct_esp_vert_high_2011ct")

## lower pct_esp_vert_high_2011ct upper pct_esp_vert_high_2011ct 
##                     0.02828030                     0.03533605

ci.lmm.3 <- confint(res.lmm, "vis_minority_2011.Q:pct_esp_vert_high_2011ct")

## lower vis_minority_2011.Q:pct_esp_vert_high_2011ct 
##                                        0.002081562 
## upper vis_minority_2011.Q:pct_esp_vert_high_2011ct 
##                                        0.004598848

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei$df
.t["predict"] <- as.vector(predict(res.lmm))

g_vis_tc <- ggplot(.t, aes(y=100*predict/ct_area_hct, x=pct_esp_vert_high_2011ct, colour=factor(vis_minority_2011.Q), fill=factor(vis_minority_2011.Q))) + 
  geom_smooth(method = "lm", alpha=.1) +
  labs(colour='vis_minority_2011.Q', fill='vis_minority_2011.Q')
g_vis_tc

Interpretation of the vis_minority_2011.Q coefficient (significant): we have \(e^{-0.077}\) = 0.926 (95%CI: 0.896 – 0.957)

Coefficient interpretation (marginal + interaction) as relative risk.

# Compute combined effects (marginal + interaction) for each quintile of SES:
i_e <- data.frame(vis_minority_2011.Q=c(1,3,5))
i_e["UC2011.effect"] <- res.lmm[["fixef"]]['pct_esp_vert_high_2011ct'] + i_e["vis_minority_2011.Q"] * res.lmm[["fixef"]]['vis_minority_2011.Q:pct_esp_vert_high_2011ct']
i_e["UC2011.relative.risk"] <- exp(i_e["UC2011.effect"])
i_e

# Compute combined effects (marginal + interaction) for each quintile of SES:
i_e <- data.frame(pct_esp_vert_high_2011ct = quantile(clean_bei$df$pct_esp_vert_high_2011ct)[2:4])
i_e["SES.effect"] <- res.lmm[["fixef"]]['vis_minority_2011.Q'] + i_e["pct_esp_vert_high_2011ct"] * res.lmm[["fixef"]]['vis_minority_2011.Q:pct_esp_vert_high_2011ct']
i_e["SES.relative.risk"] <- exp(i_e["SES.effect"])
i_e

6.3 UI vs gentrified CT

Gentrified CT between 2011 and 2016

6.3.1 Bike lane length change (hurdle)

Bike lane length change

f <- Bike_lane_total.hm.2016ct ~ gentrified_2016_2011 * Bike_lane.by.street.2011ct + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm.0 <- fitme(I(Bike_lane_total.hm.2016ct != 0) ~ gentrified_2016_2011 * Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.0, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2016ct != 0) ~ gentrified_2016_2011 * Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                                                     Estimate Cond. SE t-value
## (Intercept)                                          -4.9123   0.5013 -9.7998
## gentrified_2016_2011TRUE                              0.1917   0.5944  0.3226
## Bike_lane.by.street.2011ct                            3.4688   1.4200  2.4427
## gentrified_2016_2011TRUE:Bike_lane.by.street.2011ct  -1.6031   1.6952 -0.9457
##                                                     p-value
## (Intercept)                                         0.00000
## gentrified_2016_2011TRUE                            0.74703
## Bike_lane.by.street.2011ct                          0.01458
## gentrified_2016_2011TRUE:Bike_lane.by.street.2011ct 0.34432
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1379976 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  6.356  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -146.8066

# NB: not converging
# ci.lmm.0.1 <- confint(res.lmm.0, "gentrified_2016_2011TRUE")
# ci.lmm.0.2 <- confint(res.lmm.0, "Bike_lane.by.street.2011ct")
# ci.lmm.0.3 <- confint(res.lmm.0, "gentrified_2016_2011TRUE:Bike_lane.by.street.2011ct")

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.0, plot = F)
  plot(simout)
}

# Plotting interaction || MEANINGLESS
# .t <- clean_bei$df
# .t["predict"] <- as.vector(predict(res.lmm.0))
# 
# ggplot(.t, aes(y=100*predict/street_length.hm, x=Bike_lane.by.street.2011ct, colour=factor(gentrified_2016_2011), fill=factor(gentrified_2016_2011))) + 
#   geom_smooth(method = "lm", alpha=.1) +
#   labs(colour='gentrified_2016_2011', fill='gentrified_2016_2011')

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2016ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2016ct ~ gentrified_2016_2011 * Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2016ct ~ gentrified_2016_2011 * Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                                     Estimate Cond. SE t-value
## (Intercept)                                         -2.75518 0.046857 -58.800
## gentrified_2016_2011TRUE                             0.20178 0.071981   2.803
## Bike_lane.by.street.2011ct                           0.05753 0.002441  23.564
## gentrified_2016_2011TRUE:Bike_lane.by.street.2011ct -0.01157 0.004373  -2.646
##                                                      p-value
## (Intercept)                                         0.000000
## gentrified_2016_2011TRUE                            0.005060
## Bike_lane.by.street.2011ct                          0.000000
## gentrified_2016_2011TRUE:Bike_lane.by.street.2011ct 0.008136
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1504352 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.1088  
## # of obs: 564; # of groups: ct_no, 564 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1877.541

# ci.lmm.cnt.1 <- confint(res.lmm.cnt, "gentrified_2016_2011TRUE")
# ci.lmm.cnt.2 <- confint(res.lmm.cnt, "Bike_lane.by.street.2011ct")
# ci.lmm.cnt.3 <- confint(res.lmm.cnt, "gentrified_2016_2011TRUE:Bike_lane.by.street.2011ct")

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.cnt, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei.cnt$df
.t["predict"] <- as.vector(predict(res.lmm.cnt))

g_gen_bk.hrdl <- ggplot(.t, aes(y=100*predict/street_length.hm, x=Bike_lane.by.street.2011ct, colour=factor(gentrified_2016_2011), fill=factor(gentrified_2016_2011))) + 
  geom_smooth(method = "lm", alpha=.1) +
  labs(colour='gentrified_2016_2011', fill='gentrified_2016_2011')
g_gen_bk.hrdl

# AIC
AIC(res.lmm.0)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.0$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4060.696

Interpretation of the gentrified_2016_2011 coefficient | Zero model (not significant): we have \(e^{0.192}\) = 1.211 Interpretation of the gentrified_2016_2011 coefficient | Count model (not significant): we have \(e^{0.202}\) = 1.224

6.3.2 Greenness change

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_2017ct ~ gentrified_2016_2011 * pct_esp_vert_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2017ct ~ gentrified_2016_2011 * pct_esp_vert_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2017ct ~ gentrified_2016_2011 * pct_esp_vert_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                               Estimate  Cond. SE t-value
## (Intercept)                                  -1.613014 0.0257795 -62.570
## gentrified_2016_2011TRUE                     -0.202554 0.0643593  -3.147
## pct_esp_vert_2011ct                           0.018742 0.0004559  41.105
## gentrified_2016_2011TRUE:pct_esp_vert_2011ct  0.005263 0.0016871   3.120
##                                               p-value
## (Intercept)                                  0.000000
## gentrified_2016_2011TRUE                     0.001648
## pct_esp_vert_2011ct                          0.000000
## gentrified_2016_2011TRUE:pct_esp_vert_2011ct 0.001811
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1349448 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.004838  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2012.743

ci.lmm.1 <- confint(res.lmm, "gentrified_2016_2011TRUE")

## lower gentrified_2016_2011TRUE upper gentrified_2016_2011TRUE 
##                    -0.32924546                    -0.07617365

ci.lmm.2 <- confint(res.lmm, "pct_esp_vert_2011ct")

## lower pct_esp_vert_2011ct upper pct_esp_vert_2011ct 
##                0.01782698                0.01968221

ci.lmm.3 <- confint(res.lmm, "gentrified_2016_2011TRUE:pct_esp_vert_2011ct")

## lower gentrified_2016_2011TRUE:pct_esp_vert_2011ct 
##                                        0.001943885 
## upper gentrified_2016_2011TRUE:pct_esp_vert_2011ct 
##                                        0.008578808

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei$df
.t["predict"] <- as.vector(predict(res.lmm))

g_gen_gr <- ggplot(.t, aes(y=100*predict/ct_area_hct, x=pct_esp_vert_2011ct, colour=factor(gentrified_2016_2011), fill=factor(gentrified_2016_2011))) + 
  geom_smooth(method = "lm", alpha=.1) +
  labs(colour='gentrified_2016_2011', fill='gentrified_2016_2011')
g_gen_gr

Interpretation of the gentrified_2016_2011 coefficient (significant): we have \(e^{-0.203}\) = 0.817 (95%CI: 0.719 – 0.927)

Coefficient interpretation (marginal + interaction) as relative risk.

# Compute combined effects (marginal + interaction) for each quintile of SES:
i_e <- data.frame(gentrified_2016_2011=0:1)
i_e["UC2011.effect"] <- res.lmm[["fixef"]]['pct_esp_vert_2011ct'] + i_e["gentrified_2016_2011"] * res.lmm[["fixef"]]['gentrified_2016_2011TRUE:pct_esp_vert_2011ct']
i_e["UC2011.relative.risk"] <- exp(i_e["UC2011.effect"])
i_e

# Compute combined effects (marginal + interaction) for each quintile of SES:
i_e <- data.frame(pct_esp_vert_2011ct = quantile(clean_bei$df$pct_esp_vert_2011ct)[2:4])
i_e["SES.effect"] <- res.lmm[["fixef"]]['gentrified_2016_2011TRUE'] + i_e["pct_esp_vert_2011ct"] * res.lmm[["fixef"]]['gentrified_2016_2011TRUE:pct_esp_vert_2011ct']
i_e["SES.relative.risk"] <- exp(i_e["SES.effect"])
i_e

6.3.3 Canopy (trees) change

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_high_2017ct ~ gentrified_2016_2011 * pct_esp_vert_high_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2017ct ~ gentrified_2016_2011 * pct_esp_vert_high_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2017ct ~ gentrified_2016_2011 * pct_esp_vert_high_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                                   Estimate  Cond. SE t-value
## (Intercept)                                       -2.35730 0.0279340 -84.388
## gentrified_2016_2011TRUE                          -0.20459 0.0715883  -2.858
## pct_esp_vert_high_2011ct                           0.03939 0.0009182  42.893
## gentrified_2016_2011TRUE:pct_esp_vert_high_2011ct  0.01322 0.0035508   3.722
##                                                     p-value
## (Intercept)                                       0.0000000
## gentrified_2016_2011TRUE                          0.0042654
## pct_esp_vert_high_2011ct                          0.0000000
## gentrified_2016_2011TRUE:pct_esp_vert_high_2011ct 0.0001974
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1380802 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.01222  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1814.314

ci.lmm.1 <- confint(res.lmm, "gentrified_2016_2011TRUE")

## lower gentrified_2016_2011TRUE upper gentrified_2016_2011TRUE 
##                    -0.34539306                    -0.06456076

ci.lmm.2 <- confint(res.lmm, "pct_esp_vert_high_2011ct")

## lower pct_esp_vert_high_2011ct upper pct_esp_vert_high_2011ct 
##                     0.03756862                     0.04126454

ci.lmm.3 <- confint(res.lmm, "gentrified_2016_2011TRUE:pct_esp_vert_high_2011ct")

## lower gentrified_2016_2011TRUE:pct_esp_vert_high_2011ct 
##                                             0.006232907 
## upper gentrified_2016_2011TRUE:pct_esp_vert_high_2011ct 
##                                             0.020169474

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei$df
.t["predict"] <- as.vector(predict(res.lmm))

g_gen_tc <- ggplot(.t, aes(y=100*predict/ct_area_hct, x=pct_esp_vert_high_2011ct, colour=factor(gentrified_2016_2011), fill=factor(gentrified_2016_2011))) + 
  geom_smooth(method = "lm", alpha=.1) +
  labs(colour='gentrified_2016_2011', fill='gentrified_2016_2011')
g_gen_tc

Interpretation of the gentrified_2016_2011 coefficient (significant): we have \(e^{-0.205}\) = 0.815 (95%CI: 0.708 – 0.937)

Coefficient interpretation (marginal + interaction) as relative risk.

# Compute combined effects (marginal + interaction) for each quintile of SES:
i_e <- data.frame(gentrified_2016_2011=0:1)
i_e["UC2011.effect"] <- res.lmm[["fixef"]]['pct_esp_vert_high_2011ct'] + i_e["gentrified_2016_2011"] * res.lmm[["fixef"]]['gentrified_2016_2011TRUE:pct_esp_vert_high_2011ct']
i_e["UC2011.relative.risk"] <- exp(i_e["UC2011.effect"])
i_e

# Compute combined effects (marginal + interaction) for each quintile of SES:
i_e <- data.frame(pct_esp_vert_high_2011ct = quantile(clean_bei$df$pct_esp_vert_high_2011ct)[2:4])
i_e["SES.effect"] <- res.lmm[["fixef"]]['gentrified_2016_2011TRUE'] + i_e["pct_esp_vert_high_2011ct"] * res.lmm[["fixef"]]['gentrified_2016_2011TRUE:pct_esp_vert_high_2011ct']
i_e["SES.relative.risk"] <- exp(i_e["SES.effect"])
i_e

7 Association between SES and UI | SES as categories

Following Yan and Behzad’s request, the exact same models as above are run, this time using SES quintiles as categories instead of ordinal values.

7.1 UI vs Pampalon | material

7.1.1 Bike lane length change (hurdle)

Bike lane length change

f <- Bike_lane_total.hm.2016ct ~ wSCOREMAT.2011.Q * Bike_lane.by.street.2011ct + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm.0 <- fitme(I(Bike_lane_total.hm.2016ct != 0) ~ factor(wSCOREMAT.2011.Q) * Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.0, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2016ct != 0) ~ factor(wSCOREMAT.2011.Q) * 
##     Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                                                      Estimate  Cond. SE t-value
## (Intercept)                                            -6.438 9.722e-01 -6.6221
## factor(wSCOREMAT.2011.Q)2                               1.926 1.005e+00  1.9166
## factor(wSCOREMAT.2011.Q)3                               1.830 1.084e+00  1.6888
## factor(wSCOREMAT.2011.Q)4                               1.713 1.083e+00  1.5818
## factor(wSCOREMAT.2011.Q)5                               1.119 1.025e+00  1.0914
## Bike_lane.by.street.2011ct                             54.449 1.422e+02  0.3830
## factor(wSCOREMAT.2011.Q)2:Bike_lane.by.street.2011ct  -52.827 1.422e+02 -0.3716
## factor(wSCOREMAT.2011.Q)3:Bike_lane.by.street.2011ct 6167.495 3.011e+04  0.2048
## factor(wSCOREMAT.2011.Q)4:Bike_lane.by.street.2011ct  170.855 9.721e+02  0.1758
## factor(wSCOREMAT.2011.Q)5:Bike_lane.by.street.2011ct  -52.766 1.422e+02 -0.3712
##                                                        p-value
## (Intercept)                                          3.541e-11
## factor(wSCOREMAT.2011.Q)2                            5.529e-02
## factor(wSCOREMAT.2011.Q)3                            9.126e-02
## factor(wSCOREMAT.2011.Q)4                            1.137e-01
## factor(wSCOREMAT.2011.Q)5                            2.751e-01
## Bike_lane.by.street.2011ct                           7.017e-01
## factor(wSCOREMAT.2011.Q)2:Bike_lane.by.street.2011ct 7.102e-01
## factor(wSCOREMAT.2011.Q)3:Bike_lane.by.street.2011ct 8.377e-01
## factor(wSCOREMAT.2011.Q)4:Bike_lane.by.street.2011ct 8.605e-01
## factor(wSCOREMAT.2011.Q)5:Bike_lane.by.street.2011ct 7.105e-01
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##    1.rho 
## 0.137743 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  5.117  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -142.7656

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.0, plot = F)
  plot(simout)
}

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2016ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2016ct ~ factor(wSCOREMAT.2011.Q) * Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2016ct ~ factor(wSCOREMAT.2011.Q) * Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                                       Estimate Cond. SE
## (Intercept)                                          -2.596117 0.077232
## factor(wSCOREMAT.2011.Q)2                            -0.082531 0.095227
## factor(wSCOREMAT.2011.Q)3                            -0.344225 0.101073
## factor(wSCOREMAT.2011.Q)4                            -0.169518 0.101080
## factor(wSCOREMAT.2011.Q)5                             0.019403 0.103981
## Bike_lane.by.street.2011ct                            0.049586 0.003791
## factor(wSCOREMAT.2011.Q)2:Bike_lane.by.street.2011ct  0.002008 0.005510
## factor(wSCOREMAT.2011.Q)3:Bike_lane.by.street.2011ct  0.023129 0.006319
## factor(wSCOREMAT.2011.Q)4:Bike_lane.by.street.2011ct  0.006693 0.005783
## factor(wSCOREMAT.2011.Q)5:Bike_lane.by.street.2011ct -0.004647 0.006463
##                                                       t-value   p-value
## (Intercept)                                          -33.6146 0.0000000
## factor(wSCOREMAT.2011.Q)2                             -0.8667 0.3861205
## factor(wSCOREMAT.2011.Q)3                             -3.4057 0.0006599
## factor(wSCOREMAT.2011.Q)4                             -1.6771 0.0935277
## factor(wSCOREMAT.2011.Q)5                              0.1866 0.8519723
## Bike_lane.by.street.2011ct                            13.0796 0.0000000
## factor(wSCOREMAT.2011.Q)2:Bike_lane.by.street.2011ct   0.3645 0.7154798
## factor(wSCOREMAT.2011.Q)3:Bike_lane.by.street.2011ct   3.6605 0.0002517
## factor(wSCOREMAT.2011.Q)4:Bike_lane.by.street.2011ct   1.1573 0.2471496
## factor(wSCOREMAT.2011.Q)5:Bike_lane.by.street.2011ct  -0.7190 0.4721634
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1503961 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.1058  
## # of obs: 564; # of groups: ct_no, 564 
##  ------------- Likelihood values  -------------
##                        logLik
## p_v(h) (marginal L): -1874.29

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.cnt, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei.cnt$df
.t["predict"] <- as.vector(predict(res.lmm.cnt))

g_mat_bk.hrdl <- ggplot(.t, aes(y=100*predict/street_length.hm, x=Bike_lane.by.street.2011ct, colour=factor(wSCOREMAT.2011.Q), fill=factor(wSCOREMAT.2011.Q))) + 
  geom_smooth(method = "lm", alpha=.1, linetype="dashed") +
  labs(colour='wSCOREMAT.2011.Q', fill='wSCOREMAT.2011.Q')
g_mat_bk.hrdl

# AIC
AIC(res.lmm.0)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.0$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4058.111

7.1.2 Greenness change

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_2017ct ~ wSCOREMAT.2011.Q * pct_esp_vert_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2017ct ~ factor(wSCOREMAT.2011.Q)* pct_esp_vert_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2017ct ~ factor(wSCOREMAT.2011.Q) * pct_esp_vert_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                                 Estimate  Cond. SE  t-value
## (Intercept)                                   -1.4971348 0.0460467 -32.5134
## factor(wSCOREMAT.2011.Q)2                     -0.1162630 0.0618502  -1.8797
## factor(wSCOREMAT.2011.Q)3                     -0.0825597 0.0634354  -1.3015
## factor(wSCOREMAT.2011.Q)4                     -0.1729263 0.0685627  -2.5222
## factor(wSCOREMAT.2011.Q)5                     -0.4873193 0.0840536  -5.7977
## pct_esp_vert_2011ct                            0.0171251 0.0007596  22.5460
## factor(wSCOREMAT.2011.Q)2:pct_esp_vert_2011ct  0.0014829 0.0010502   1.4119
## factor(wSCOREMAT.2011.Q)3:pct_esp_vert_2011ct  0.0009409 0.0011150   0.8438
## factor(wSCOREMAT.2011.Q)4:pct_esp_vert_2011ct  0.0029923 0.0013692   2.1854
## factor(wSCOREMAT.2011.Q)5:pct_esp_vert_2011ct  0.0119756 0.0022691   5.2778
##                                                 p-value
## (Intercept)                                   0.000e+00
## factor(wSCOREMAT.2011.Q)2                     6.014e-02
## factor(wSCOREMAT.2011.Q)3                     1.931e-01
## factor(wSCOREMAT.2011.Q)4                     1.166e-02
## factor(wSCOREMAT.2011.Q)5                     6.722e-09
## pct_esp_vert_2011ct                           0.000e+00
## factor(wSCOREMAT.2011.Q)2:pct_esp_vert_2011ct 1.580e-01
## factor(wSCOREMAT.2011.Q)3:pct_esp_vert_2011ct 3.988e-01
## factor(wSCOREMAT.2011.Q)4:pct_esp_vert_2011ct 2.886e-02
## factor(wSCOREMAT.2011.Q)5:pct_esp_vert_2011ct 1.308e-07
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1367616 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.004266  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2000.254

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei$df
.t["predict"] <- as.vector(predict(res.lmm))

g_mat_gr <- ggplot(.t, aes(y=100*predict/ct_area_hct, x=pct_esp_vert_2011ct, colour=factor(wSCOREMAT.2011.Q), fill=factor(wSCOREMAT.2011.Q))) + 
  geom_smooth(method = "lm", alpha=.1) +
  labs(colour='wSCOREMAT.2011.Q', fill='wSCOREMAT.2011.Q')
g_mat_gr

7.1.3 Canopy (trees) change

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_high_2017ct ~ wSCOREMAT.2011.Q * pct_esp_vert_high_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2017ct ~ factor(wSCOREMAT.2011.Q) * pct_esp_vert_high_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2017ct ~ factor(wSCOREMAT.2011.Q) * pct_esp_vert_high_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                                     Estimate Cond. SE t-value
## (Intercept)                                        -2.195912 0.043413 -50.582
## factor(wSCOREMAT.2011.Q)2                          -0.170865 0.062582  -2.730
## factor(wSCOREMAT.2011.Q)3                          -0.176232 0.065792  -2.679
## factor(wSCOREMAT.2011.Q)4                          -0.331512 0.070623  -4.694
## factor(wSCOREMAT.2011.Q)5                          -0.749906 0.089324  -8.395
## pct_esp_vert_high_2011ct                            0.033787 0.001234  27.370
## factor(wSCOREMAT.2011.Q)2:pct_esp_vert_high_2011ct  0.007058 0.002075   3.401
## factor(wSCOREMAT.2011.Q)3:pct_esp_vert_high_2011ct  0.006521 0.002386   2.734
## factor(wSCOREMAT.2011.Q)4:pct_esp_vert_high_2011ct  0.015541 0.002997   5.185
## factor(wSCOREMAT.2011.Q)5:pct_esp_vert_high_2011ct  0.042632 0.005363   7.949
##                                                      p-value
## (Intercept)                                        0.000e+00
## factor(wSCOREMAT.2011.Q)2                          6.328e-03
## factor(wSCOREMAT.2011.Q)3                          7.393e-03
## factor(wSCOREMAT.2011.Q)4                          2.677e-06
## factor(wSCOREMAT.2011.Q)5                          0.000e+00
## pct_esp_vert_high_2011ct                           0.000e+00
## factor(wSCOREMAT.2011.Q)2:pct_esp_vert_high_2011ct 6.706e-04
## factor(wSCOREMAT.2011.Q)3:pct_esp_vert_high_2011ct 6.262e-03
## factor(wSCOREMAT.2011.Q)4:pct_esp_vert_high_2011ct 2.158e-07
## factor(wSCOREMAT.2011.Q)5:pct_esp_vert_high_2011ct 1.887e-15
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1379822 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.009176  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1780.152

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei$df
.t["predict"] <- as.vector(predict(res.lmm))

g_mat_tc <- ggplot(.t, aes(y=100*predict/ct_area_hct, x=pct_esp_vert_high_2011ct, colour=factor(wSCOREMAT.2011.Q), fill=factor(wSCOREMAT.2011.Q))) + 
  geom_smooth(method = "lm", alpha=.1) +
  labs(colour='wSCOREMAT.2011.Q', fill='wSCOREMAT.2011.Q')
g_mat_tc

7.2 UI vs Visible minority

7.2.1 Bike lane length change (hurdle)

Bike lane length change

f <- Bike_lane_total.hm.2016ct ~ vis_minority_2011.Q * Bike_lane.by.street.2011ct + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm.0 <- fitme(I(Bike_lane_total.hm.2016ct != 0) ~ factor(vis_minority_2011.Q) * Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.0, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2016ct != 0) ~ factor(vis_minority_2011.Q) * 
##     Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                                                         Estimate Cond. SE
## (Intercept)                                               -5.705    1.227
## factor(vis_minority_2011.Q)2                               1.711    1.401
## factor(vis_minority_2011.Q)3                               2.099    1.340
## factor(vis_minority_2011.Q)4                              -0.692    1.451
## factor(vis_minority_2011.Q)5                              -1.040    1.346
## Bike_lane.by.street.2011ct                                63.221  369.060
## factor(vis_minority_2011.Q)2:Bike_lane.by.street.2011ct  343.774 8009.562
## factor(vis_minority_2011.Q)3:Bike_lane.by.street.2011ct  -60.791  369.066
## factor(vis_minority_2011.Q)4:Bike_lane.by.street.2011ct  418.608 4648.758
## factor(vis_minority_2011.Q)5:Bike_lane.by.street.2011ct  -60.552  369.061
##                                                          t-value   p-value
## (Intercept)                                             -4.65042 3.313e-06
## factor(vis_minority_2011.Q)2                             1.22111 2.220e-01
## factor(vis_minority_2011.Q)3                             1.56680 1.172e-01
## factor(vis_minority_2011.Q)4                            -0.47704 6.333e-01
## factor(vis_minority_2011.Q)5                            -0.77282 4.396e-01
## Bike_lane.by.street.2011ct                               0.17130 8.640e-01
## factor(vis_minority_2011.Q)2:Bike_lane.by.street.2011ct  0.04292 9.658e-01
## factor(vis_minority_2011.Q)3:Bike_lane.by.street.2011ct -0.16472 8.692e-01
## factor(vis_minority_2011.Q)4:Bike_lane.by.street.2011ct  0.09005 9.282e-01
## factor(vis_minority_2011.Q)5:Bike_lane.by.street.2011ct -0.16407 8.697e-01
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1378827 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  11.6  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -137.7682

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.0, plot = F)
  plot(simout)
}

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2016ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2016ct ~ factor(vis_minority_2011.Q) * Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2016ct ~ factor(vis_minority_2011.Q) * Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                                          Estimate Cond. SE
## (Intercept)                                             -2.600489 0.078225
## factor(vis_minority_2011.Q)2                            -0.114586 0.096774
## factor(vis_minority_2011.Q)3                            -0.129058 0.100608
## factor(vis_minority_2011.Q)4                            -0.250708 0.104275
## factor(vis_minority_2011.Q)5                            -0.028887 0.107428
## Bike_lane.by.street.2011ct                               0.051362 0.004280
## factor(vis_minority_2011.Q)2:Bike_lane.by.street.2011ct  0.003173 0.005676
## factor(vis_minority_2011.Q)3:Bike_lane.by.street.2011ct  0.006144 0.006687
## factor(vis_minority_2011.Q)4:Bike_lane.by.street.2011ct  0.012759 0.006636
## factor(vis_minority_2011.Q)5:Bike_lane.by.street.2011ct -0.005974 0.006801
##                                                          t-value p-value
## (Intercept)                                             -33.2439 0.00000
## factor(vis_minority_2011.Q)2                             -1.1840 0.23639
## factor(vis_minority_2011.Q)3                             -1.2828 0.19957
## factor(vis_minority_2011.Q)4                             -2.4043 0.01620
## factor(vis_minority_2011.Q)5                             -0.2689 0.78801
## Bike_lane.by.street.2011ct                               11.9997 0.00000
## factor(vis_minority_2011.Q)2:Bike_lane.by.street.2011ct   0.5590 0.57613
## factor(vis_minority_2011.Q)3:Bike_lane.by.street.2011ct   0.9189 0.35817
## factor(vis_minority_2011.Q)4:Bike_lane.by.street.2011ct   1.9229 0.05449
## factor(vis_minority_2011.Q)5:Bike_lane.by.street.2011ct  -0.8785 0.37969
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1504866 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.1102  
## # of obs: 564; # of groups: ct_no, 564 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1876.529

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm.cnt, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei.cnt$df
.t["predict"] <- as.vector(predict(res.lmm.cnt))

g_vis_bk.hrdl <- ggplot(.t, aes(y=100*predict/street_length.hm, x=Bike_lane.by.street.2011ct, colour=factor(vis_minority_2011.Q), fill=factor(vis_minority_2011.Q))) + 
  geom_smooth(method = "lm", alpha=.1, linetype = "dashed") +
  labs(colour='vis_minority_2011.Q', fill='vis_minority_2011.Q')
g_vis_bk.hrdl

# AIC
AIC(res.lmm.0)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.0$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4052.594

7.2.2 Greenness change

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_2017ct ~ vis_minority_2011.Q * pct_esp_vert_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2017ct ~ factor(vis_minority_2011.Q) * pct_esp_vert_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2017ct ~ factor(vis_minority_2011.Q) * pct_esp_vert_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                                   Estimate  Cond. SE t-value
## (Intercept)                                      -1.501387 0.0461251 -32.550
## factor(vis_minority_2011.Q)2                     -0.126758 0.0617600  -2.052
## factor(vis_minority_2011.Q)3                     -0.119219 0.0673443  -1.770
## factor(vis_minority_2011.Q)4                     -0.150541 0.0621047  -2.424
## factor(vis_minority_2011.Q)5                     -0.327300 0.0697281  -4.694
## pct_esp_vert_2011ct                               0.017003 0.0007648  22.233
## factor(vis_minority_2011.Q)2:pct_esp_vert_2011ct  0.001859 0.0010595   1.755
## factor(vis_minority_2011.Q)3:pct_esp_vert_2011ct  0.002070 0.0012848   1.611
## factor(vis_minority_2011.Q)4:pct_esp_vert_2011ct  0.002399 0.0011290   2.125
## factor(vis_minority_2011.Q)5:pct_esp_vert_2011ct  0.006502 0.0014860   4.375
##                                                    p-value
## (Intercept)                                      0.000e+00
## factor(vis_minority_2011.Q)2                     4.013e-02
## factor(vis_minority_2011.Q)3                     7.668e-02
## factor(vis_minority_2011.Q)4                     1.535e-02
## factor(vis_minority_2011.Q)5                     2.680e-06
## pct_esp_vert_2011ct                              0.000e+00
## factor(vis_minority_2011.Q)2:pct_esp_vert_2011ct 7.932e-02
## factor(vis_minority_2011.Q)3:pct_esp_vert_2011ct 1.071e-01
## factor(vis_minority_2011.Q)4:pct_esp_vert_2011ct 3.357e-02
## factor(vis_minority_2011.Q)5:pct_esp_vert_2011ct 1.213e-05
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1358167 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.0045  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2006.416

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei$df
.t["predict"] <- as.vector(predict(res.lmm))

g_vis_gr <- ggplot(.t, aes(y=100*predict/ct_area_hct, x=pct_esp_vert_2011ct, colour=factor(vis_minority_2011.Q), fill=factor(vis_minority_2011.Q))) + 
  geom_smooth(method = "lm", alpha=.1) +
  labs(colour='vis_minority_2011.Q', fill='vis_minority_2011.Q')
g_vis_gr

7.2.3 Canopy (trees) change

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_high_2017ct ~ vis_minority_2011.Q * pct_esp_vert_high_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2017ct ~ factor(vis_minority_2011.Q) * pct_esp_vert_high_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2017ct ~ factor(vis_minority_2011.Q) * pct_esp_vert_high_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                                         Estimate Cond. SE
## (Intercept)                                           -2.2494769 0.047193
## factor(vis_minority_2011.Q)2                          -0.1218389 0.064577
## factor(vis_minority_2011.Q)3                           0.0146893 0.066527
## factor(vis_minority_2011.Q)4                          -0.2778787 0.065932
## factor(vis_minority_2011.Q)5                          -0.3623408 0.077380
## pct_esp_vert_high_2011ct                               0.0357059 0.001466
## factor(vis_minority_2011.Q)2:pct_esp_vert_high_2011ct  0.0041755 0.002176
## factor(vis_minority_2011.Q)3:pct_esp_vert_high_2011ct -0.0007537 0.002489
## factor(vis_minority_2011.Q)4:pct_esp_vert_high_2011ct  0.0108121 0.002458
## factor(vis_minority_2011.Q)5:pct_esp_vert_high_2011ct  0.0171154 0.003341
##                                                        t-value   p-value
## (Intercept)                                           -47.6658 0.000e+00
## factor(vis_minority_2011.Q)2                           -1.8867 5.920e-02
## factor(vis_minority_2011.Q)3                            0.2208 8.252e-01
## factor(vis_minority_2011.Q)4                           -4.2147 2.502e-05
## factor(vis_minority_2011.Q)5                           -4.6826 2.832e-06
## pct_esp_vert_high_2011ct                               24.3551 0.000e+00
## factor(vis_minority_2011.Q)2:pct_esp_vert_high_2011ct   1.9187 5.502e-02
## factor(vis_minority_2011.Q)3:pct_esp_vert_high_2011ct  -0.3028 7.620e-01
## factor(vis_minority_2011.Q)4:pct_esp_vert_high_2011ct   4.3986 1.089e-05
## factor(vis_minority_2011.Q)5:pct_esp_vert_high_2011ct   5.1230 3.007e-07
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1380247 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.01063  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1799.683

if (plot.resid) {
  simout <- simulateResiduals(fittedModel = res.lmm, plot = F)
  plot(simout)
}

# Plotting interaction
.t <- clean_bei$df
.t["predict"] <- as.vector(predict(res.lmm))

g_vis_tc <- ggplot(.t, aes(y=100*predict/ct_area_hct, x=pct_esp_vert_high_2011ct, colour=factor(vis_minority_2011.Q), fill=factor(vis_minority_2011.Q))) + 
  geom_smooth(method = "lm", alpha=.1) +
  labs(colour='vis_minority_2011.Q', fill='vis_minority_2011.Q')
g_vis_tc

7.3 UI vs gentrified CT

No new models here, as gentrified variable is already used as a pure categorical variable.

8 Association between SES and UI | Main effect, no interaction

As discussed with Yan and Behzad, we rerun the UI models, without the interaction term \(SES \times UC_{2011}\)

8.1 UI vs Pampalon | material

8.1.1 Bike lane length change (hurdle)

Bike lane length change

f <- Bike_lane_total.hm.2016ct ~ wSCOREMAT.2011.Q + Bike_lane.by.street.2011ct + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm.zero <- fitme(I(Bike_lane_total.hm.2016ct != 0) ~ wSCOREMAT.2011.Q + Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.zero, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2016ct != 0) ~ wSCOREMAT.2011.Q + Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                             Estimate Cond. SE  t-value   p-value
## (Intercept)                -4.939506   0.8771 -5.63191 1.782e-08
## wSCOREMAT.2011.Q            0.003004   0.2117  0.01419 9.887e-01
## Bike_lane.by.street.2011ct  2.499779   0.6984  3.57955 3.442e-04
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1377147 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  5.786  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -149.7332

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2016ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2016ct ~ wSCOREMAT.2011.Q + Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2016ct ~ wSCOREMAT.2011.Q + Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                             Estimate Cond. SE  t-value p-value
## (Intercept)                -2.677404 0.068370 -39.1606  0.0000
## wSCOREMAT.2011.Q           -0.007146 0.016550  -0.4318  0.6659
## Bike_lane.by.street.2011ct  0.054017 0.002135  25.2953  0.0000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1502893 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.1125  
## # of obs: 564; # of groups: ct_no, 564 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1884.431

# AIC
AIC(res.lmm.zero)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.zero$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4078.329

Transforming the model coefficients (continuous):

# Zero model
round(exp(res.lmm.zero[["fixef"]]), 3) %>%
  knitr::kable(caption="Zero model transformed coeffs")

Zero model transformed coeffs

	x
(Intercept)	0.007
wSCOREMAT.2011.Q	1.003
Bike_lane.by.street.2011ct	12.180

# Count model
round(exp(res.lmm.cnt[["fixef"]]), 3) %>%
  knitr::kable(caption="Count model transformed coeffs")

Count model transformed coeffs

	x
(Intercept)	0.069
wSCOREMAT.2011.Q	0.993
Bike_lane.by.street.2011ct	1.056

8.1.2 Greenness change

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_2017ct ~ wSCOREMAT.2011.Q + pct_esp_vert_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2017ct ~ wSCOREMAT.2011.Q + pct_esp_vert_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2017ct ~ wSCOREMAT.2011.Q + pct_esp_vert_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                     Estimate  Cond. SE t-value p-value
## (Intercept)         -1.58398 0.0342580  -46.24  0.0000
## wSCOREMAT.2011.Q    -0.01166 0.0058884   -1.98  0.0477
## pct_esp_vert_2011ct  0.01875 0.0004615   40.63  0.0000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1359291 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.004773  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                        logLik
## p_v(h) (marginal L): -2016.65

# Wald-test p-value for wSCOREMAT.2011.Q close to threshold, using LRT to improve accuracy
res.lmm.0 <- update(res.lmm, . ~ . -wSCOREMAT.2011.Q)
LRT(res.lmm.0, res.lmm)

##      chi2_LR df    p_value
## p_v 3.792348  1 0.05148739

Transforming the model coefficients (continuous):

round(exp(res.lmm[["fixef"]]), 3) %>%
  knitr::kable(caption="Transformed coeffs")

Transformed coeffs

	x
(Intercept)	0.205
wSCOREMAT.2011.Q	0.988
pct_esp_vert_2011ct	1.019

8.1.3 Canopy (trees) change

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_high_2017ct ~ wSCOREMAT.2011.Q + pct_esp_vert_high_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2017ct ~ wSCOREMAT.2011.Q + pct_esp_vert_high_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2017ct ~ wSCOREMAT.2011.Q + pct_esp_vert_high_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                          Estimate  Cond. SE t-value p-value
## (Intercept)              -2.32838 0.0424926 -54.795  0.0000
## wSCOREMAT.2011.Q         -0.01022 0.0090720  -1.126  0.2601
## pct_esp_vert_high_2011ct  0.03961 0.0009664  40.985  0.0000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1378526 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.01294  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1823.392

Transforming the model coefficients (continuous):

round(exp(res.lmm[["fixef"]]), 3) %>%
  knitr::kable(caption="Transformed coeffs")

Transformed coeffs

	x
(Intercept)	0.097
wSCOREMAT.2011.Q	0.990
pct_esp_vert_high_2011ct	1.040

8.2 UI vs Visible minority

8.2.1 Bike lane length change (hurdle)

Bike lane length change

f <- Bike_lane_total.hm.2016ct ~ vis_minority_2011.Q + Bike_lane.by.street.2011ct + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm.zero <- fitme(I(Bike_lane_total.hm.2016ct != 0) ~ vis_minority_2011.Q + Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.zero, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2016ct != 0) ~ vis_minority_2011.Q + Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                            Estimate Cond. SE t-value   p-value
## (Intercept)                  -3.072   0.9195  -3.341 0.0008351
## vis_minority_2011.Q          -0.516   0.2337  -2.208 0.0272372
## Bike_lane.by.street.2011ct    2.861   0.8191   3.493 0.0004782
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1378998 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  6.963  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -145.6995

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2016ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2016ct ~ vis_minority_2011.Q + Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2016ct ~ vis_minority_2011.Q + Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                            Estimate Cond. SE t-value p-value
## (Intercept)                -2.63391 0.069833 -37.717  0.0000
## vis_minority_2011.Q        -0.02109 0.017257  -1.222  0.2216
## Bike_lane.by.street.2011ct  0.05408 0.002161  25.023  0.0000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1504889 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.1121  
## # of obs: 564; # of groups: ct_no, 564 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1880.959

# AIC
AIC(res.lmm.zero)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.zero$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4063.317

Transforming the model coefficients (continuous):

# Zero model
round(exp(res.lmm.zero[["fixef"]]), 3) %>%
  knitr::kable(caption="Zero model transformed coeffs")

Zero model transformed coeffs

	x
(Intercept)	0.046
vis_minority_2011.Q	0.597
Bike_lane.by.street.2011ct	17.474

# Count model
round(exp(res.lmm.cnt[["fixef"]]), 3) %>%
  knitr::kable(caption="Count model transformed coeffs")

Count model transformed coeffs

	x
(Intercept)	0.072
vis_minority_2011.Q	0.979
Bike_lane.by.street.2011ct	1.056

8.2.2 Greenness change

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_2017ct ~ vis_minority_2011.Q + pct_esp_vert_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2017ct ~ vis_minority_2011.Q + pct_esp_vert_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2017ct ~ vis_minority_2011.Q + pct_esp_vert_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                      Estimate  Cond. SE t-value p-value
## (Intercept)         -1.608537 0.0323275 -49.757  0.0000
## vis_minority_2011.Q -0.007267 0.0057005  -1.275  0.2023
## pct_esp_vert_2011ct  0.018988 0.0004481  42.376  0.0000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1358025 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.004891  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2016.956

Transforming the model coefficients (continuous):

round(exp(res.lmm[["fixef"]]), 3) %>%
  knitr::kable(caption="Transformed coeffs")

Transformed coeffs

	x
(Intercept)	0.200
vis_minority_2011.Q	0.993
pct_esp_vert_2011ct	1.019

8.2.3 Canopy (trees) change

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_high_2017ct ~ vis_minority_2011.Q + pct_esp_vert_high_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2017ct ~ vis_minority_2011.Q + pct_esp_vert_high_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2017ct ~ vis_minority_2011.Q + pct_esp_vert_high_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                           Estimate  Cond. SE  t-value p-value
## (Intercept)              -2.356969 0.0402505 -58.5575  0.0000
## vis_minority_2011.Q      -0.002609 0.0088099  -0.2961  0.7672
## pct_esp_vert_high_2011ct  0.039985 0.0009402  42.5293  0.0000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##    1.rho 
## 0.138067 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.01303  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1821.833

Transforming the model coefficients (continuous):

round(exp(res.lmm[["fixef"]]), 3) %>%
  knitr::kable(caption="Transformed coeffs")

Transformed coeffs

	x
(Intercept)	0.095
vis_minority_2011.Q	0.997
pct_esp_vert_high_2011ct	1.041

8.3 UI vs gentrified CT

Gentrified CT between 2011 and 2016

8.3.1 Bike lane length change (hurdle)

Bike lane length change

f <- Bike_lane_total.hm.2016ct ~ gentrified_2016_2011 + Bike_lane.by.street.2011ct + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm.zero <- fitme(I(Bike_lane_total.hm.2016ct != 0) ~ gentrified_2016_2011 + Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.zero, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2016ct != 0) ~ gentrified_2016_2011 + Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                            Estimate Cond. SE t-value   p-value
## (Intercept)                -4.82263   0.5165 -9.3369 0.0000000
## gentrified_2016_2011TRUE   -0.07812   0.6074 -0.1286 0.8976627
## Bike_lane.by.street.2011ct  2.81386   0.8174  3.4424 0.0005766
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1380204 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  7.002  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -147.7386

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2016ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2016ct ~ gentrified_2016_2011 + Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2016ct ~ gentrified_2016_2011 + Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                            Estimate Cond. SE t-value p-value
## (Intercept)                -2.71508  0.04457 -60.912  0.0000
## gentrified_2016_2011TRUE    0.05633  0.04724   1.192  0.2331
## Bike_lane.by.street.2011ct  0.05436  0.00214  25.397  0.0000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##    1.rho 
## 0.150439 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.1116  
## # of obs: 564; # of groups: ct_no, 564 
##  ------------- Likelihood values  -------------
##                      logLik
## p_v(h) (marginal L):  -1881

# AIC
AIC(res.lmm.zero)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.zero$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4067.478

Transforming the model coefficients:

# Zero model
round(exp(res.lmm.zero[["fixef"]]), 3) %>%
  knitr::kable(caption="Zero model transformed coeffs")

Zero model transformed coeffs

	x
(Intercept)	0.008
gentrified_2016_2011TRUE	0.925
Bike_lane.by.street.2011ct	16.674

# Count model
round(exp(res.lmm.cnt[["fixef"]]), 3) %>%
  knitr::kable(caption="Count model transformed coeffs")

Count model transformed coeffs

	x
(Intercept)	0.066
gentrified_2016_2011TRUE	1.058
Bike_lane.by.street.2011ct	1.056

8.3.2 Greenness change

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_2017ct ~ gentrified_2016_2011 + pct_esp_vert_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2017ct ~ gentrified_2016_2011 + pct_esp_vert_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2017ct ~ gentrified_2016_2011 + pct_esp_vert_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                          Estimate  Cond. SE  t-value p-value
## (Intercept)              -1.63121 0.0255404 -63.8681   0.000
## gentrified_2016_2011TRUE -0.01288 0.0206032  -0.6249   0.532
## pct_esp_vert_2011ct       0.01909 0.0004486  42.5552   0.000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1360243 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.004979  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2017.555

Transforming the model coefficients:

round(exp(res.lmm[["fixef"]]), 3) %>%
  knitr::kable(caption="Transformed coeffs")

Transformed coeffs

	x
(Intercept)	0.196
gentrified_2016_2011TRUE	0.987
pct_esp_vert_2011ct	1.019

8.3.3 Canopy (trees) change

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_high_2017ct ~ gentrified_2016_2011 + pct_esp_vert_high_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2017ct ~ gentrified_2016_2011 + pct_esp_vert_high_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2017ct ~ gentrified_2016_2011 + pct_esp_vert_high_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                          Estimate  Cond. SE t-value p-value
## (Intercept)              -2.37670 0.0279253 -85.109  0.0000
## gentrified_2016_2011TRUE  0.03580 0.0293925   1.218  0.2233
## pct_esp_vert_high_2011ct  0.04024 0.0009101  44.218  0.0000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1380247 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.01293  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1821.142

Transforming the model coefficients:

round(exp(res.lmm[["fixef"]]), 3) %>%
  knitr::kable(caption="Transformed coeffs")

Transformed coeffs

	x
(Intercept)	0.093
gentrified_2016_2011TRUE	1.036
pct_esp_vert_high_2011ct	1.041

9 Association between SES and UI | Main effect, no interaction, SES as categories

As discussed with Yan and Behzad, we rerun the UI models, without the interaction term \(SES \times UC_{2011}\), SES as categories instaed of continuous

9.1 UI vs Pampalon | material

9.1.1 Bike lane length change (hurdle)

Bike lane length change

f <- Bike_lane_total.hm.2016ct ~ factor(wSCOREMAT.2011.Q) + Bike_lane.by.street.2011ct + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm.zero <- fitme(I(Bike_lane_total.hm.2016ct != 0) ~ factor(wSCOREMAT.2011.Q) + Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.zero, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2016ct != 0) ~ factor(wSCOREMAT.2011.Q) + 
##     Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                            Estimate Cond. SE t-value   p-value
## (Intercept)                 -6.3848   1.0783 -5.9213 3.195e-09
## factor(wSCOREMAT.2011.Q)2    1.7251   1.1184  1.5425 1.230e-01
## factor(wSCOREMAT.2011.Q)3    2.1681   1.1958  1.8131 6.981e-02
## factor(wSCOREMAT.2011.Q)4    1.9986   1.1962  1.6709 9.475e-02
## factor(wSCOREMAT.2011.Q)5    0.7114   1.1433  0.6222 5.338e-01
## Bike_lane.by.street.2011ct   2.7278   0.8021  3.4007 6.722e-04
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1376078 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  7.864  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -147.1698

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2016ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2016ct ~ factor(wSCOREMAT.2011.Q) + Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2016ct ~ factor(wSCOREMAT.2011.Q) + Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                             Estimate Cond. SE   t-value p-value
## (Intercept)                -2.661013 0.062493 -42.58081  0.0000
## factor(wSCOREMAT.2011.Q)2  -0.039221 0.061482  -0.63793  0.5235
## factor(wSCOREMAT.2011.Q)3  -0.072592 0.063707  -1.13947  0.2545
## factor(wSCOREMAT.2011.Q)4  -0.074928 0.065152  -1.15005  0.2501
## factor(wSCOREMAT.2011.Q)5  -0.004295 0.073100  -0.05875  0.9531
## Bike_lane.by.street.2011ct  0.054073 0.002142  25.24000  0.0000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1503103 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.112  
## # of obs: 564; # of groups: ct_no, 564 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1883.302

# AIC
AIC(res.lmm.zero)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.zero$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4076.943

Transforming the model coefficients (categorical):

# Zero model
round(exp(res.lmm.zero[["fixef"]]), 3) %>%
  knitr::kable(caption="Zero model transformed coeffs")

Zero model transformed coeffs

	x
(Intercept)	0.002
factor(wSCOREMAT.2011.Q)2	5.613
factor(wSCOREMAT.2011.Q)3	8.742
factor(wSCOREMAT.2011.Q)4	7.379
factor(wSCOREMAT.2011.Q)5	2.037
Bike_lane.by.street.2011ct	15.300

# Count model
round(exp(res.lmm.cnt[["fixef"]]), 3) %>%
  knitr::kable(caption="Count model transformed coeffs")

Count model transformed coeffs

	x
(Intercept)	0.070
factor(wSCOREMAT.2011.Q)2	0.962
factor(wSCOREMAT.2011.Q)3	0.930
factor(wSCOREMAT.2011.Q)4	0.928
factor(wSCOREMAT.2011.Q)5	0.996
Bike_lane.by.street.2011ct	1.056

9.1.2 Greenness change

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_2017ct ~ factor(wSCOREMAT.2011.Q) + pct_esp_vert_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2017ct ~ factor(wSCOREMAT.2011.Q) + pct_esp_vert_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2017ct ~ factor(wSCOREMAT.2011.Q) + pct_esp_vert_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                           Estimate  Cond. SE t-value  p-value
## (Intercept)               -1.58982 0.0305516 -52.037 0.000000
## factor(wSCOREMAT.2011.Q)2 -0.03055 0.0189787  -1.609 0.107508
## factor(wSCOREMAT.2011.Q)3 -0.02366 0.0203601  -1.162 0.245144
## factor(wSCOREMAT.2011.Q)4 -0.02242 0.0222606  -1.007 0.313861
## factor(wSCOREMAT.2011.Q)5 -0.06958 0.0269580  -2.581 0.009854
## pct_esp_vert_2011ct        0.01872 0.0004635  40.389 0.000000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1358061 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.004722  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2014.941

Transforming the model coefficients (categorical):

round(exp(res.lmm[["fixef"]]), 3) %>%
  knitr::kable(caption="Transformed coeffs")

Transformed coeffs

	x
(Intercept)	0.204
factor(wSCOREMAT.2011.Q)2	0.970
factor(wSCOREMAT.2011.Q)3	0.977
factor(wSCOREMAT.2011.Q)4	0.978
factor(wSCOREMAT.2011.Q)5	0.933
pct_esp_vert_2011ct	1.019

9.1.3 Canopy (trees) change

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_high_2017ct ~ factor(wSCOREMAT.2011.Q) + pct_esp_vert_high_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2017ct ~ factor(wSCOREMAT.2011.Q) + pct_esp_vert_high_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2017ct ~ factor(wSCOREMAT.2011.Q) + pct_esp_vert_high_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                           Estimate  Cond. SE  t-value p-value
## (Intercept)               -2.36271 0.0374207 -63.1390 0.00000
## factor(wSCOREMAT.2011.Q)2  0.03639 0.0293902   1.2383 0.21560
## factor(wSCOREMAT.2011.Q)3  0.02160 0.0318033   0.6791 0.49710
## factor(wSCOREMAT.2011.Q)4  0.02420 0.0345149   0.7011 0.48325
## factor(wSCOREMAT.2011.Q)5 -0.07695 0.0416488  -1.8475 0.06467
## pct_esp_vert_high_2011ct   0.03951 0.0009565  41.3107 0.00000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1378409 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.01245  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1819.267

Transforming the model coefficients (categorical):

round(exp(res.lmm[["fixef"]]), 3) %>%
  knitr::kable(caption="Transformed coeffs")

Transformed coeffs

	x
(Intercept)	0.094
factor(wSCOREMAT.2011.Q)2	1.037
factor(wSCOREMAT.2011.Q)3	1.022
factor(wSCOREMAT.2011.Q)4	1.024
factor(wSCOREMAT.2011.Q)5	0.926
pct_esp_vert_high_2011ct	1.040

9.2 UI vs Visible minority

9.2.1 Bike lane length change (hurdle)

Bike lane length change

f <- Bike_lane_total.hm.2016ct ~ factor(vis_minority_2011.Q) + Bike_lane.by.street.2011ct + offset(log(street_length.hm))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm.zero <- fitme(I(Bike_lane_total.hm.2016ct != 0) ~ factor(vis_minority_2011.Q) + Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = binomial())
summary(res.lmm.zero, details = c(p_value="Wald"))

## formula: I(Bike_lane_total.hm.2016ct != 0) ~ factor(vis_minority_2011.Q) + 
##     Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + 
##     adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: binomial( link = logit ) 
##  ------------ Fixed effects (beta) ------------
##                              Estimate Cond. SE t-value   p-value
## (Intercept)                   -5.0763    1.144  -4.436 9.180e-06
## factor(vis_minority_2011.Q)2   1.4928    1.316   1.135 2.565e-01
## factor(vis_minority_2011.Q)3   1.3100    1.253   1.046 2.958e-01
## factor(vis_minority_2011.Q)4   0.1949    1.300   0.150 8.808e-01
## factor(vis_minority_2011.Q)5  -1.6542    1.276  -1.297 1.948e-01
## Bike_lane.by.street.2011ct     3.2327    1.019   3.174 1.505e-03
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1378309 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  11.06  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -143.4633

# Count model (Poisson)
clean_bei.cnt <- bei_df_aoi %>%
  filter(Bike_lane_total.hm.2016ct != 0) %>%
  tidy_df(CT16, f)

res.lmm.cnt <- fitme(Bike_lane_total.hm.2016ct ~ factor(vis_minority_2011.Q) + Bike_lane.by.street.2011ct + offset(log(street_length.hm)) + adjacency(1|ct_no),
                 data = clean_bei.cnt$df, adjMatrix = clean_bei.cnt$nbmatx,
                 family = Tpoisson())
summary(res.lmm.cnt, details = c(p_value="Wald"))

## formula: Bike_lane_total.hm.2016ct ~ factor(vis_minority_2011.Q) + Bike_lane.by.street.2011ct + 
##     offset(log(street_length.hm)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: 0-truncated poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                              Estimate Cond. SE  t-value p-value
## (Intercept)                  -2.63738 0.061277 -43.0402  0.0000
## factor(vis_minority_2011.Q)2 -0.07088 0.059733  -1.1866  0.2354
## factor(vis_minority_2011.Q)3 -0.05550 0.063083  -0.8798  0.3790
## factor(vis_minority_2011.Q)4 -0.10233 0.066387  -1.5414  0.1232
## factor(vis_minority_2011.Q)5 -0.08137 0.074967  -1.0854  0.2778
## Bike_lane.by.street.2011ct    0.05428 0.002169  25.0282  0.0000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1504811 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.1117  
## # of obs: 564; # of groups: ct_no, 564 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1880.374

# AIC
AIC(res.lmm.zero)
AIC(res.lmm.cnt)

# Combined AIC
"Combined Hurdle AIC:"

## [1] "Combined Hurdle AIC:"

-2 * res.lmm.zero$APHLs$p_v - 2 * res.lmm.cnt$APHLs$p_v + 2 * Reduce(sum, res.lmm.cnt$dfs)

## [1] 4063.675

Transforming the model coefficients (categorical):

# Zero model
round(exp(res.lmm.zero[["fixef"]]), 3) %>%
  knitr::kable(caption="Zero model transformed coeffs")

Zero model transformed coeffs

	x
(Intercept)	0.006
factor(vis_minority_2011.Q)2	4.450
factor(vis_minority_2011.Q)3	3.706
factor(vis_minority_2011.Q)4	1.215
factor(vis_minority_2011.Q)5	0.191
Bike_lane.by.street.2011ct	25.349

# Count model
round(exp(res.lmm.cnt[["fixef"]]), 3) %>%
  knitr::kable(caption="Count model transformed coeffs")

Count model transformed coeffs

	x
(Intercept)	0.072
factor(vis_minority_2011.Q)2	0.932
factor(vis_minority_2011.Q)3	0.946
factor(vis_minority_2011.Q)4	0.903
factor(vis_minority_2011.Q)5	0.922
Bike_lane.by.street.2011ct	1.056

9.2.2 Greenness change

Measuring canopy (i.e. greenness ~ grass & trees) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_2017ct ~ factor(vis_minority_2011.Q) + pct_esp_vert_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_2017ct ~ factor(vis_minority_2011.Q) + pct_esp_vert_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_2017ct ~ factor(vis_minority_2011.Q) + pct_esp_vert_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                                Estimate  Cond. SE   t-value p-value
## (Intercept)                  -1.6151901 0.0296830 -54.41456  0.0000
## factor(vis_minority_2011.Q)2 -0.0190763 0.0195996  -0.97330  0.3304
## factor(vis_minority_2011.Q)3 -0.0005607 0.0216980  -0.02584  0.9794
## factor(vis_minority_2011.Q)4 -0.0183082 0.0215032  -0.85142  0.3945
## factor(vis_minority_2011.Q)5 -0.0396666 0.0254609  -1.55794  0.1192
## pct_esp_vert_2011ct           0.0189953 0.0004495  42.26227  0.0000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##    1.rho 
## 0.135867 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.004871  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -2015.997

Transforming the model coefficients (categorical):

round(exp(res.lmm[["fixef"]]), 3) %>%
  knitr::kable(caption="Transformed coeffs")

Transformed coeffs

	x
(Intercept)	0.199
factor(vis_minority_2011.Q)2	0.981
factor(vis_minority_2011.Q)3	0.999
factor(vis_minority_2011.Q)4	0.982
factor(vis_minority_2011.Q)5	0.961
pct_esp_vert_2011ct	1.019

9.2.3 Canopy (trees) change

Measuring high canopy (i.e. trees only) ratio within CT/buffer in 2011 (in %) at the Census tract level

f <- area_esp_vert_high_2017ct ~ factor(vis_minority_2011.Q) + pct_esp_vert_high_2011ct + offset(log(ct_area_hct))

clean_bei <- tidy_df(bei_df_aoi, CT16, f)

res.lmm <- fitme(area_esp_vert_high_2017ct ~ factor(vis_minority_2011.Q) + pct_esp_vert_high_2011ct + offset(log(ct_area_hct)) + adjacency(1|ct_no),
                 data = clean_bei$df, adjMatrix = clean_bei$nbmatx,
                 family = poisson())
summary(res.lmm, details = c(p_value="Wald"))

## formula: area_esp_vert_high_2017ct ~ factor(vis_minority_2011.Q) + pct_esp_vert_high_2011ct + 
##     offset(log(ct_area_hct)) + adjacency(1 | ct_no)
## Estimation of corrPars and lambda by Laplace ML approximation (p_v).
## Estimation of fixed effects by Laplace ML approximation (p_v).
## Estimation of lambda by 'outer' ML, maximizing p_v.
## family: poisson( link = log ) 
##  ------------ Fixed effects (beta) ------------
##                               Estimate  Cond. SE   t-value p-value
## (Intercept)                  -2.365558 0.0357953 -66.08573  0.0000
## factor(vis_minority_2011.Q)2 -0.001358 0.0302778  -0.04486  0.9642
## factor(vis_minority_2011.Q)3  0.033812 0.0330881   1.02189  0.3068
## factor(vis_minority_2011.Q)4 -0.018870 0.0337475  -0.55914  0.5761
## factor(vis_minority_2011.Q)5 -0.006233 0.0387782  -0.16073  0.8723
## pct_esp_vert_high_2011ct      0.039999 0.0009377  42.65560  0.0000
##  --------------- Random effects ---------------
## Family: gaussian( link = identity ) 
##                    --- Correlation parameters:
##     1.rho 
## 0.1380643 
##            --- Variance parameters ('lambda'):
## lambda = var(u) for u ~ Gaussian; 
##    ct_no  :  0.0129  
## # of obs: 688; # of groups: ct_no, 688 
##  ------------- Likelihood values  -------------
##                         logLik
## p_v(h) (marginal L): -1820.503

Transforming the model coefficients (categorical):

round(exp(res.lmm[["fixef"]]), 3) %>%
  knitr::kable(caption="Transformed coeffs")

Transformed coeffs

	x
(Intercept)	0.094
factor(vis_minority_2011.Q)2	0.999
factor(vis_minority_2011.Q)3	1.034
factor(vis_minority_2011.Q)4	0.981
factor(vis_minority_2011.Q)5	0.994
pct_esp_vert_high_2011ct	1.041

9.3 UI vs gentrified CT

No new models here, as gentrified variable is already used as a pure categorical variable.

10 Summary of association between SES and Built Environment

NOTICE: This section needs to be updated

Presenting interaction terms (STROBE and more specifically here): best practice suggests we should include interaction terms for specific values of covariates.

SES metric	BE metric	UC 2011 trend	UI 2011 -> 2016 trend (SES effect only, no interaction)
Pampalon / MAT 2011 (zero + cnt)	Bike lane	0.790 (p=0.016) & 0.954 (p=0.031*)	1.054 (p=0.807) & 0.992 (p=0.723)
Pampalon / MAT 2011	Greenness	0.911 (p<0.001)	0.940 (p<0.001)
Pampalon / MAT 2011	Tree canopy	0.879 (p<0.001)	0.888 (p<0.001)
Visible Minority 2011 (zero + cnt)	Bike lane	0.809 (p=0.018) & 0.933 (p=0.016)	0.623 (p=0.061*) & 0.979 (p=0.401)
Visible Minority 2011	Greenness	0.934 (p<0.001)	0.943 (p<0.001)
Visible Minority 2011	Tree canopy	0.896 (p<0.001)	0.926 (p<0.001)
Gentrified 2011-2016 (zero + cnt)	Bike lane	0.936 (p=0.789) & 1.1 (p=0.236)	1.211 (p=0.747) & 1.224 (p=0.005)
Gentrified 2011-2016	Greenness	0.822 (p<0.001)	0.817 (p=0.002)
Gentrified 2011-2016	Tree canopy	0.86 (p=0.003)	0.815 (p=0.004)

p-values: Wald t-tests except when p-value close to threshold where Likelihood ratio test has been used (marked with *) Bold: significant

11 Tables and figures

11.1 Maps of BEC and BEI

# Green space
g_bec_bike <- ggplot() +
   geom_sf(data=filter(bike_lane_changes, interact_aoi), mapping = aes(fill=as.numeric(Bike_lane.by.street.2011ct)), lwd = 0) +
  scale_fill_distiller(name = "Bike lane to\nstreet length (%)", palette = "YlGn", direction = 1) + 
   geom_sf(data=filter(CT16, interact_aoi), fill=NA, color="gray", size=.2, alpha=0.2) + 
  ggnewscale::new_scale_fill() +
  geom_sf(data=filter(bike_lane_changes, interact_aoi), mapping = aes(fill=factor(units::drop_units(Bike_lane.by.street.2011ct) == 0)), lwd = 0.1) +
  scale_fill_manual(name="No bike lane in CT", values = c("TRUE" = "white"), labels=NULL, na.translate = FALSE) +
  labs(title = "Normalized bike lane length in 2011")


g_bei_bike <- ggplot() +
  geom_sf(data=filter(bike_lane_changes, interact_aoi), mapping = aes(fill=as.numeric(Bike_lane_diff.by.street.2011.2016ct)), lwd=0) +
   geom_sf(data=filter(CT16, interact_aoi), fill=NA, color="gray", size=.2, alpha=0.2) + 
  scale_fill_gradient2(name = "Change in normalized\nbike lane (%)")+ 
  labs(title = "Bike lane change between 2011 and 2016")

# Green space
g_bec_green <- ggplot() +
   geom_sf(data=inner_join(filter(CT16, interact_aoi), esp_vert_ct, by="GeoUID"), mapping = aes(fill=as.numeric(pct_esp_vert_2011)), lwd = 0) +
   geom_sf(data=filter(CT16, interact_aoi), fill=NA, color="gray", size=.2, alpha=0.2) + 
  scale_fill_distiller(name = "Greenspace (%)", palette = "BrBG", direction = 1)+ 
  labs(title = "Proportion of greenspace in 2011")

g_bei_green <- ggplot() +
   geom_sf(data=inner_join(filter(CT16, interact_aoi), esp_vert_ct, by="GeoUID"), mapping = aes(fill=as.numeric(pct_esp_vert_diff_2011.2017)), lwd = 0) +
   geom_sf(data=filter(CT16, interact_aoi), fill=NA, color="gray", size=.2, alpha=0.2) + 
  scale_fill_gradient2(name = "Greenspace\nchange (%)")+ 
  labs(title = "Greenspace change between 2011 and 2017")

# Green space
g_bec_tree <- ggplot() +
   geom_sf(data=inner_join(filter(CT16, interact_aoi), esp_vert_ct, by="GeoUID"), mapping = aes(fill=as.numeric(pct_esp_vert_high_2011)), lwd = 0) +
   geom_sf(data=filter(CT16, interact_aoi), fill=NA, color="gray", size=.2, alpha=0.2) + 
  scale_fill_distiller(name = "Tree canopy (%)", palette = "BrBG", direction = 1)+ 
  labs(title = "Proportion of tree canopy in 2011")

g_bei_tree <- ggplot() +
   geom_sf(data=inner_join(filter(CT16, interact_aoi), esp_vert_ct, by="GeoUID"), mapping = aes(fill=as.numeric(pct_esp_vert_diff_high_2011.2017)), lwd = 0) +
   geom_sf(data=filter(CT16, interact_aoi), fill=NA, color="gray", size=.2, alpha=0.2) + 
  scale_fill_gradient2(name = "Tree canopy\nchange (%)")+ 
  labs(title = "Tree canopy change between 2011 and 2017")

# Create grid of maps
pcol1 <- plot_grid(
  g_bec_bike + theme_void(), 
  g_bec_green + theme_void(), 
  g_bec_tree + theme_void(),
  align = "vh",
  labels = c("A", "B", "C"),
  hjust = -1,
  ncol = 1
)

pcol2 <- plot_grid(
  g_bei_bike + theme_void(), 
  g_bei_green + theme_void(), 
  g_bei_tree + theme_void(),
  align = "vh",
  #labels = c("D", "E", "F"),
  hjust = -1,
  ncol = 1
)

# output all graphs
plot_grid(pcol1, pcol2, nrow=1)

11.2 SES and BEI outcomes

# Extract SES and BEI in 2011
.tab1_2011 <- bei_df_aoi %>%
  transmute(year = "2011",
            zone = zone,
            CT_UID = CT_UID,
            Population = Population,
            `Material score` = wSCOREMAT.2011,
            `% visible minorities` = vis_minority_2011,
            `gentrified` = gentrified_2016_2011,
            `Bike lane` = Bike_lane_total.2011ct > 0,
            `Bike lane length (hm)` = Bike_lane_total.2011ct/100,
            `% Bike lane to streets` = Bike_lane.by.street.2011ct,
            `Green space area (ha)` = area_esp_vert_2011ct,
            `% green space within CT` = pct_esp_vert_2011ct,
            `Tree canopy area (ha)` = area_esp_vert_high_2011ct,
            `% tree canopy within CT` = pct_esp_vert_high_2011ct)

# Extract SES and BEI in 2016
.tab1_2016 <- bei_df_aoi %>%
  transmute(year = "2016",
            zone = zone,
            CT_UID = CT_UID,
            `Bike lane` = Bike_lane_total.2016ct > 0,
            `Bike lane length (hm)` = Bike_lane_total.2016ct/100,
            `% Bike lane to streets` = Bike_lane.by.street.2016ct,
            `Green space area (ha)` = area_esp_vert_2017ct,
            `% green space within CT` = pct_esp_vert_2017ct,
            `Tree canopy area (ha)` = area_esp_vert_high_2017ct,
            `% tree canopy within CT` = pct_esp_vert_high_2017ct)

.tab1_med <- bind_rows(.tab1_2011, .tab1_2016) %>%
  group_by(year) %>%
  summarize(across(where(is.numeric), median, na.rm=TRUE), 
            `% gentrified` = 100 * sum(`gentrified`, na.rm = TRUE) / n(),
            `Bike lane presence` = sum(`Bike lane`))
.tab1_p25 <- bind_rows(.tab1_2011, .tab1_2016) %>%
  group_by(year) %>%
  summarize(across(where(is.numeric), quantile, probs=.25, na.rm=TRUE))
.tab1_p75 <- bind_rows(.tab1_2011, .tab1_2016) %>%
  group_by(year) %>%
  summarize(across(where(is.numeric), quantile, probs=.75, na.rm=TRUE))
tab1 <- inner_join(.tab1_med, .tab1_p25, by="year", suffix = c("", " p25")) %>%
  inner_join(.tab1_p75, by="year", suffix = c("", " p75")) %>%
  transmute(year = year,
            Population = case_when(year == "2016" ~ "", 
                                   TRUE ~ paste0(round(`Population`,1), " (", round(`Population p25`,1), " - ", round(`Population p75`,1), ")")),
            `Material score` = case_when(year == "2016" ~ "", 
                                         TRUE ~ paste0(round(`Material score`,3), " (", round(`Material score p25`,3), " - ", round(`Material score p75`,3), ")")),
            `% visible minorities` = case_when(is.na(`% visible minorities`) ~ "", 
                                               TRUE ~ paste0(round(`% visible minorities`,1), " (", round(`% visible minorities p25`,1), " - ", round(`% visible minorities p75`,1), ")")),
            `% gentrified CTs` = case_when(year == "2016" ~ "", 
                                           TRUE ~ as.character(round(`% gentrified`, 1))),
            `Bike lane presence (N)` = as.character(`Bike lane presence`),
            `Bike lane length (hm)` = paste0(round(`Bike lane length (hm)`,1), " (", round(`Bike lane length (hm) p25`,1), " - ", round(`Bike lane length (hm) p75`,1), ")"),
            `% Bike lane to streets` = paste0(round(`% Bike lane to streets`,1), " (", round(`% Bike lane to streets p25`,1), " - ", round(`% Bike lane to streets p75`,1), ")"),
            `Green space area (ha)` = paste0(round(`Green space area (ha)`,1), " (", round(`Green space area (ha) p25`,1), " - ", round(`Green space area (ha) p75`,1), ")"),
            `% green space within CT` = paste0(round(`% green space within CT`,1), " (", round(`% green space within CT p25`,1), " - ", round(`% green space within CT p75`,1), ")"),
            `Tree canopy area (ha)` = paste0(round(`Tree canopy area (ha)`,1), " (", round(`Tree canopy area (ha) p25`,1), " - ", round(`Tree canopy area (ha) p75`,1), ")"),
            `% tree canopy within CT` = paste0(round(`% tree canopy within CT`,1), " (", round(`% tree canopy within CT p25`,1), " - ", round(`% tree canopy within CT p75`,1), ")")) %>%
  tibble::column_to_rownames("year") %>%
  t() %>% 
  as.data.frame()

tab1 %>% knitr::kable() %>%
  kableExtra::kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))

	2011	2016
Population	3812 (2628 - 5157)
Material score	0.006 (-0.019 - 0.031)
% visible minorities	21.3 (13.9 - 34.1)
% gentrified CTs	29.5
Bike lane presence (N)	503	592
Bike lane length (hm)	6.9 (0 - 18.5)	10.7 (3 - 22.2)
% Bike lane to streets	7 (0 - 14)	10.9 (3.8 - 18.2)
Green space area (ha)	23 (8 - 64)	26 (10 - 68)
% green space within CT	36 (24.7 - 47.4)	40.7 (29.5 - 51)
Tree canopy area (ha)	11 (4 - 24)	12 (5 - 28)
% tree canopy within CT	16.4 (11.8 - 22.6)	20.2 (14.5 - 26.8)

11.2.1 By Q1 / Q5

We look at Urban conditions in 2011 and 2016 within Q1 and Q5 of 2011 equity metrics

# Extract SES and BEI in 2011
.tab1_2011 <- bei_df_aoi %>%
  filter(wSCOREMAT.2011.Q %in% c(1, 5) ) %>%
  transmute(year = "2011",
            quintile = case_when(wSCOREMAT.2011.Q == 1 ~ "Q1 Deprivation",
                                 wSCOREMAT.2011.Q == 5 ~ "Q5 Deprivation"),
            zone = zone,
            CT_UID = CT_UID,
            Population = Population,
            `Material score` = wSCOREMAT.2011,
            `% visible minorities` = vis_minority_2011,
            `gentrified` = gentrified_2016_2011,
            `Bike lane` = Bike_lane_total.2011ct > 0,
            `Bike lane length (hm)` = Bike_lane_total.2011ct/100,
            `% Bike lane to streets` = Bike_lane.by.street.2011ct,
            `Green space area (ha)` = area_esp_vert_2011ct,
            `% green space within CT` = pct_esp_vert_2011ct,
            `Tree canopy area (ha)` = area_esp_vert_high_2011ct,
            `% tree canopy within CT` = pct_esp_vert_high_2011ct)

# Extract SES and BEI in 2016
.tab1_2016 <- bei_df_aoi %>%
  filter(wSCOREMAT.2011.Q %in% c(1, 5) ) %>%
  transmute(year = "2016",
            quintile = case_when(wSCOREMAT.2011.Q == 1 ~ "Q1 Deprivation",
                                 wSCOREMAT.2011.Q == 5 ~ "Q5 Deprivation"),
            zone = zone,
            CT_UID = CT_UID,
            `Bike lane` = Bike_lane_total.2016ct > 0,
            `Bike lane length (hm)` = Bike_lane_total.2016ct/100,
            `% Bike lane to streets` = Bike_lane.by.street.2016ct,
            `Green space area (ha)` = area_esp_vert_2017ct,
            `% green space within CT` = pct_esp_vert_2017ct,
            `Tree canopy area (ha)` = area_esp_vert_high_2017ct,
            `% tree canopy within CT` = pct_esp_vert_high_2017ct)

.tab1_med <- bind_rows(.tab1_2011, .tab1_2016) %>%
  group_by(year, quintile) %>%
  summarize(across(where(is.numeric), median, na.rm=TRUE), 
            `% gentrified` = 100 * sum(`gentrified`, na.rm = TRUE) / n(),
            `Bike lane presence` = sum(`Bike lane`),
            `Bike lane absence` = n() - sum(`Bike lane`))

## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

.tab1_p25 <- bind_rows(.tab1_2011, .tab1_2016) %>%
  group_by(year, quintile) %>%
  summarize(across(where(is.numeric), quantile, probs=.25, na.rm=TRUE))

## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

.tab1_p75 <- bind_rows(.tab1_2011, .tab1_2016) %>%
  group_by(year, quintile) %>%
  summarize(across(where(is.numeric), quantile, probs=.75, na.rm=TRUE))

## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

tab1 <- inner_join(.tab1_med, .tab1_p25, by=c("year", "quintile"), suffix = c("", " p25")) %>%
  inner_join(.tab1_p75, by=c("year", "quintile"), suffix = c("", " p75")) %>%
  transmute(year.quintile = paste(year, quintile),
            Population = case_when(year == "2016" ~ "", 
                                   TRUE ~ paste0(round(`Population`,1), " (", round(`Population p25`,1), " - ", round(`Population p75`,1), ")")),
            `Material score` = case_when(year == "2016" ~ "", 
                                         TRUE ~ paste0(round(`Material score`,3), " (", round(`Material score p25`,3), " - ", round(`Material score p75`,3), ")")),
            `% visible minorities` = case_when(is.na(`% visible minorities`) ~ "", 
                                               TRUE ~ paste0(round(`% visible minorities`,1), " (", round(`% visible minorities p25`,1), " - ", round(`% visible minorities p75`,1), ")")),
            `% gentrified CTs` = case_when(year == "2016" ~ "", 
                                           TRUE ~ as.character(round(`% gentrified`, 1))),
            `Bike lane presence (N)` = as.character(`Bike lane presence`),
            `Bike lane absence (N)` = as.character(`Bike lane absence`),
            `Bike lane length (hm)` = paste0(round(`Bike lane length (hm)`,1), " (", round(`Bike lane length (hm) p25`,1), " - ", round(`Bike lane length (hm) p75`,1), ")"),
            `% Bike lane to streets` = paste0(round(`% Bike lane to streets`,1), " (", round(`% Bike lane to streets p25`,1), " - ", round(`% Bike lane to streets p75`,1), ")"),
            `Green space area (ha)` = paste0(round(`Green space area (ha)`,1), " (", round(`Green space area (ha) p25`,1), " - ", round(`Green space area (ha) p75`,1), ")"),
            `% green space within CT` = paste0(round(`% green space within CT`,1), " (", round(`% green space within CT p25`,1), " - ", round(`% green space within CT p75`,1), ")"),
            `Tree canopy area (ha)` = paste0(round(`Tree canopy area (ha)`,1), " (", round(`Tree canopy area (ha) p25`,1), " - ", round(`Tree canopy area (ha) p75`,1), ")"),
            `% tree canopy within CT` = paste0(round(`% tree canopy within CT`,1), " (", round(`% tree canopy within CT p25`,1), " - ", round(`% tree canopy within CT p75`,1), ")")) %>%
  tibble::column_to_rownames("year.quintile") %>%
  t() %>% 
  as.data.frame()

tab1 %>% knitr::kable() %>%
  kableExtra::kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))

	2011 Q1 Deprivation	2011 Q5 Deprivation	2016 Q1 Deprivation	2016 Q5 Deprivation
year	2011	2011	2016	2016
Population	3149 (2026.8 - 5017.8)	3904.5 (2978.8 - 5212.2)
Material score	-0.046 (-0.061 - -0.037)	0.054 (0.045 - 0.07)
% visible minorities	12.8 (7.9 - 21.1)	37.1 (25.3 - 54.4)
% gentrified CTs	13	40.6
Bike lane presence (N)	106	78	116	99
Bike lane absence (N)	32	60	22	39
Bike lane length (hm)	9.3 (0 - 31.9)	2 (0 - 9.1)	11.3 (3.3 - 40.3)	5.6 (0 - 12.6)
% Bike lane to streets	8.2 (0 - 18.2)	2.4 (0 - 9.8)	12.2 (4.5 - 21.7)	8.1 (0 - 15.1)
Green space area (ha)	31 (5.2 - 116)	15.5 (7 - 24.8)	36 (7 - 119.8)	17 (8 - 28)
% green space within CT	44.5 (26.1 - 54.6)	29.1 (20.9 - 35.2)	49.9 (31.2 - 59.1)	33.3 (25 - 40.9)
Tree canopy area (ha)	15 (4 - 48.8)	7 (4 - 10)	19.5 (5 - 54.5)	8 (5 - 11.8)
% tree canopy within CT	22 (14.5 - 34.2)	12.8 (9 - 16)	28.2 (18.2 - 37.4)	15.9 (10.6 - 19.7)

# Extract SES and BEI in 2011
.tab1_2011 <- bei_df_aoi %>%
  filter(vis_minority_2011.Q %in% c(1, 5) ) %>%
  transmute(year = "2011",
            quintile = case_when(vis_minority_2011.Q == 1 ~ "Q1 Vis. Minorities",
                                 vis_minority_2011.Q == 5 ~ "Q5 Vis. Minorities"),
            zone = zone,
            CT_UID = CT_UID,
            Population = Population,
            `Material score` = wSCOREMAT.2011,
            `% visible minorities` = vis_minority_2011,
            `gentrified` = gentrified_2016_2011,
            `Bike lane` = Bike_lane_total.2011ct > 0,
            `Bike lane length (hm)` = Bike_lane_total.2011ct/100,
            `% Bike lane to streets` = Bike_lane.by.street.2011ct,
            `Green space area (ha)` = area_esp_vert_2011ct,
            `% green space within CT` = pct_esp_vert_2011ct,
            `Tree canopy area (ha)` = area_esp_vert_high_2011ct,
            `% tree canopy within CT` = pct_esp_vert_high_2011ct)

# Extract SES and BEI in 2016
.tab1_2016 <- bei_df_aoi %>%
  filter(vis_minority_2011.Q %in% c(1, 5) ) %>%
  transmute(year = "2016",
            quintile = case_when(vis_minority_2011.Q == 1 ~ "Q1 Vis. Minorities",
                                 vis_minority_2011.Q == 5 ~ "Q5 Vis. Minorities"),
            zone = zone,
            CT_UID = CT_UID,
            `Bike lane` = Bike_lane_total.2016ct > 0,
            `Bike lane length (hm)` = Bike_lane_total.2016ct/100,
            `% Bike lane to streets` = Bike_lane.by.street.2016ct,
            `Green space area (ha)` = area_esp_vert_2017ct,
            `% green space within CT` = pct_esp_vert_2017ct,
            `Tree canopy area (ha)` = area_esp_vert_high_2017ct,
            `% tree canopy within CT` = pct_esp_vert_high_2017ct)

.tab1_med <- bind_rows(.tab1_2011, .tab1_2016) %>%
  group_by(year, quintile) %>%
  summarize(across(where(is.numeric), median, na.rm=TRUE), 
            `% gentrified` = 100 * sum(`gentrified`, na.rm = TRUE) / n(),
            `Bike lane presence` = sum(`Bike lane`),
            `Bike lane absence` = n() - sum(`Bike lane`))

## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

.tab1_p25 <- bind_rows(.tab1_2011, .tab1_2016) %>%
  group_by(year, quintile) %>%
  summarize(across(where(is.numeric), quantile, probs=.25, na.rm=TRUE))

## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

.tab1_p75 <- bind_rows(.tab1_2011, .tab1_2016) %>%
  group_by(year, quintile) %>%
  summarize(across(where(is.numeric), quantile, probs=.75, na.rm=TRUE))

## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

tab1 <- inner_join(.tab1_med, .tab1_p25, by=c("year", "quintile"), suffix = c("", " p25")) %>%
  inner_join(.tab1_p75, by=c("year", "quintile"), suffix = c("", " p75")) %>%
  transmute(year.quintile = paste(year, quintile),
            Population = case_when(year == "2016" ~ "", 
                                   TRUE ~ paste0(round(`Population`,1), " (", round(`Population p25`,1), " - ", round(`Population p75`,1), ")")),
            `Material score` = case_when(year == "2016" ~ "", 
                                         TRUE ~ paste0(round(`Material score`,3), " (", round(`Material score p25`,3), " - ", round(`Material score p75`,3), ")")),
            `% visible minorities` = case_when(is.na(`% visible minorities`) ~ "", 
                                               TRUE ~ paste0(round(`% visible minorities`,1), " (", round(`% visible minorities p25`,1), " - ", round(`% visible minorities p75`,1), ")")),
            `% gentrified CTs` = case_when(year == "2016" ~ "", 
                                           TRUE ~ as.character(round(`% gentrified`, 1))),
            `Bike lane presence (N)` = as.character(`Bike lane presence`),
            `Bike lane absence (N)` = as.character(`Bike lane absence`),
            `Bike lane length (hm)` = paste0(round(`Bike lane length (hm)`,1), " (", round(`Bike lane length (hm) p25`,1), " - ", round(`Bike lane length (hm) p75`,1), ")"),
            `% Bike lane to streets` = paste0(round(`% Bike lane to streets`,1), " (", round(`% Bike lane to streets p25`,1), " - ", round(`% Bike lane to streets p75`,1), ")"),
            `Green space area (ha)` = paste0(round(`Green space area (ha)`,1), " (", round(`Green space area (ha) p25`,1), " - ", round(`Green space area (ha) p75`,1), ")"),
            `% green space within CT` = paste0(round(`% green space within CT`,1), " (", round(`% green space within CT p25`,1), " - ", round(`% green space within CT p75`,1), ")"),
            `Tree canopy area (ha)` = paste0(round(`Tree canopy area (ha)`,1), " (", round(`Tree canopy area (ha) p25`,1), " - ", round(`Tree canopy area (ha) p75`,1), ")"),
            `% tree canopy within CT` = paste0(round(`% tree canopy within CT`,1), " (", round(`% tree canopy within CT p25`,1), " - ", round(`% tree canopy within CT p75`,1), ")")) %>%
  tibble::column_to_rownames("year.quintile") %>%
  t() %>% 
  as.data.frame()

tab1 %>% knitr::kable() %>%
  kableExtra::kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))

	2011 Q1 Vis. Minorities	2011 Q5 Vis. Minorities	2016 Q1 Vis. Minorities	2016 Q5 Vis. Minorities
year	2011	2011	2016	2016
Population	3101.5 (2295.8 - 4662.2)	4139 (3391.2 - 5594.5)
Material score	-0.023 (-0.044 - 0.008)	0.037 (0.011 - 0.064)
% visible minorities	8.5 (6.2 - 10.6)	48.6 (42.3 - 58)
% gentrified CTs	29.7	29
Bike lane presence (N)	104	77	120	95
Bike lane absence (N)	34	61	18	43
Bike lane length (hm)	8.9 (0 - 30.9)	2.2 (0 - 9.8)	13.1 (5 - 35.9)	5.2 (0 - 14.7)
% Bike lane to streets	8.3 (0 - 15.4)	2.2 (0 - 8.9)	13.9 (7.4 - 21.2)	6.8 (0 - 14.4)
Green space area (ha)	26.5 (7 - 116.8)	16 (7.2 - 32.5)	29 (9 - 120.8)	18.5 (9.2 - 36.8)
% green space within CT	39.8 (26.5 - 56.7)	30.4 (23 - 38.3)	44.3 (33 - 60.1)	35.8 (26.9 - 44.6)
Tree canopy area (ha)	12.5 (4 - 48.5)	7 (4 - 15)	15 (5.2 - 53.8)	9.5 (4 - 17)
% tree canopy within CT	19.1 (14.6 - 29.8)	14.5 (8.6 - 20.6)	23.4 (18.1 - 34.1)	17.4 (9.9 - 24.2)

11.2.2 By gentrification status

# Extract SES and BEI in 2011
.tab1_2011 <- bei_df_aoi %>%
  transmute(year = "2011",
            quintile = case_when(gentrified_2016_2011 ~ "Gentrified",
                                 TRUE ~ "Not gentrified"),
            zone = zone,
            CT_UID = CT_UID,
            Population = Population,
            `Material score` = wSCOREMAT.2011,
            `% visible minorities` = vis_minority_2011,
            `gentrified` = gentrified_2016_2011,
            `Bike lane` = Bike_lane_total.2011ct > 0,
            `Bike lane length (hm)` = Bike_lane_total.2011ct/100,
            `% Bike lane to streets` = Bike_lane.by.street.2011ct,
            `Green space area (ha)` = area_esp_vert_2011ct,
            `% green space within CT` = pct_esp_vert_2011ct,
            `Tree canopy area (ha)` = area_esp_vert_high_2011ct,
            `% tree canopy within CT` = pct_esp_vert_high_2011ct)

# Extract SES and BEI in 2016
.tab1_2016 <- bei_df_aoi %>%
  transmute(year = "2016",
            quintile = case_when(gentrified_2016_2011 ~ "Gentrified",
                                 TRUE ~ "Not gentrified"),
            zone = zone,
            CT_UID = CT_UID,
            `Bike lane` = Bike_lane_total.2016ct > 0,
            `Bike lane length (hm)` = Bike_lane_total.2016ct/100,
            `% Bike lane to streets` = Bike_lane.by.street.2016ct,
            `Green space area (ha)` = area_esp_vert_2017ct,
            `% green space within CT` = pct_esp_vert_2017ct,
            `Tree canopy area (ha)` = area_esp_vert_high_2017ct,
            `% tree canopy within CT` = pct_esp_vert_high_2017ct)

.tab1_med <- bind_rows(.tab1_2011, .tab1_2016) %>%
  group_by(year, quintile) %>%
  summarize(across(where(is.numeric), median, na.rm=TRUE), 
            `% gentrified` = 100 * sum(`gentrified`, na.rm = TRUE) / n(),
            `Bike lane presence` = sum(`Bike lane`),
            `Bike lane absence` = n() - sum(`Bike lane`))

## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

.tab1_p25 <- bind_rows(.tab1_2011, .tab1_2016) %>%
  group_by(year, quintile) %>%
  summarize(across(where(is.numeric), quantile, probs=.25, na.rm=TRUE))

## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

.tab1_p75 <- bind_rows(.tab1_2011, .tab1_2016) %>%
  group_by(year, quintile) %>%
  summarize(across(where(is.numeric), quantile, probs=.75, na.rm=TRUE))

## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

tab1 <- inner_join(.tab1_med, .tab1_p25, by=c("year", "quintile"), suffix = c("", " p25")) %>%
  inner_join(.tab1_p75, by=c("year", "quintile"), suffix = c("", " p75")) %>%
  transmute(year.quintile = paste(year, quintile),
            Population = case_when(year == "2016" ~ "", 
                                   TRUE ~ paste0(round(`Population`,1), " (", round(`Population p25`,1), " - ", round(`Population p75`,1), ")")),
            `Material score` = case_when(year == "2016" ~ "", 
                                         TRUE ~ paste0(round(`Material score`,3), " (", round(`Material score p25`,3), " - ", round(`Material score p75`,3), ")")),
            `% visible minorities` = case_when(is.na(`% visible minorities`) ~ "", 
                                               TRUE ~ paste0(round(`% visible minorities`,1), " (", round(`% visible minorities p25`,1), " - ", round(`% visible minorities p75`,1), ")")),
            `% gentrified CTs` = case_when(year == "2016" ~ "", 
                                           TRUE ~ as.character(round(`% gentrified`, 1))),
            `Bike lane presence (N)` = as.character(`Bike lane presence`),
            `Bike lane absence (N)` = as.character(`Bike lane absence`),
            `Bike lane length (hm)` = paste0(round(`Bike lane length (hm)`,1), " (", round(`Bike lane length (hm) p25`,1), " - ", round(`Bike lane length (hm) p75`,1), ")"),
            `% Bike lane to streets` = paste0(round(`% Bike lane to streets`,1), " (", round(`% Bike lane to streets p25`,1), " - ", round(`% Bike lane to streets p75`,1), ")"),
            `Green space area (ha)` = paste0(round(`Green space area (ha)`,1), " (", round(`Green space area (ha) p25`,1), " - ", round(`Green space area (ha) p75`,1), ")"),
            `% green space within CT` = paste0(round(`% green space within CT`,1), " (", round(`% green space within CT p25`,1), " - ", round(`% green space within CT p75`,1), ")"),
            `Tree canopy area (ha)` = paste0(round(`Tree canopy area (ha)`,1), " (", round(`Tree canopy area (ha) p25`,1), " - ", round(`Tree canopy area (ha) p75`,1), ")"),
            `% tree canopy within CT` = paste0(round(`% tree canopy within CT`,1), " (", round(`% tree canopy within CT p25`,1), " - ", round(`% tree canopy within CT p75`,1), ")")) %>%
  tibble::column_to_rownames("year.quintile") %>%
  t() %>% 
  as.data.frame()

tab1 %>% knitr::kable() %>%
  kableExtra::kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))

	2011 Gentrified	2011 Not gentrified	2016 Gentrified	2016 Not gentrified
year	2011	2011	2016	2016
Population	3159.5 (2266.8 - 4505.8)	4043 (2862 - 5345)
Material score	0.018 (-0.004 - 0.039)	0.002 (-0.026 - 0.027)
% visible minorities	21 (13.9 - 32.4)	21.7 (14.5 - 34.7)
% gentrified CTs	100	0
Bike lane presence (N)	130	373	171	421
Bike lane absence (N)	78	124	37	76
Bike lane length (hm)	3.7 (0 - 11)	9.1 (0 - 23.5)	8 (2.4 - 15.4)	12.5 (3.7 - 26.8)
% Bike lane to streets	5.9 (0 - 14.4)	7.1 (0 - 13.7)	13.3 (3.9 - 19.8)	10.1 (3.7 - 17.6)
Green space area (ha)	9 (4 - 22.2)	34 (15 - 84)	10.5 (5 - 25.2)	38 (17 - 87)
% green space within CT	27.5 (20.7 - 35.3)	40.5 (29.1 - 51.3)	32.8 (25.7 - 40.6)	44.7 (34 - 54.6)
Tree canopy area (ha)	5 (3 - 10)	14 (6 - 33)	6 (4 - 12)	17 (8 - 37)
% tree canopy within CT	15.2 (11.4 - 19.5)	17 (11.9 - 24.2)	19.4 (15 - 23.8)	20.7 (14.1 - 28.4)

11.3 Interactions in UI associations

# extract the legend from one of the plots
legend.row1 <- get_legend(
  # create some space to the left of the legend
  g_mat_gr + labs(colour='Material score\n(Quintiles)', fill='Material score\n(Quintiles)') + theme(legend.box.margin = margin(0, 0, 0, 12))
)

prow1.1 <- plot_grid(
  g_mat_bk.hrdl + xlab("% Bike lane to streets 2011") + ylab("% Bike lane to streets 2016") + theme(legend.position = "none"),
  g_mat_gr + xlab("% green space within CT 2011") + ylab("% green space within CT 2016") + theme(legend.position = "none"),
  g_mat_tc + xlab("% tree canopy within CT 2011") + ylab("% tree canopy within CT 2016") + theme(legend.position = "none"),
  align = "vh",
  labels = c("A", "B", "C"),
  hjust = -1,
  nrow = 1
)

prow1 <- plot_grid(prow1.1, legend.row1, rel_widths = c(3, .4))

# extract the legend from one of the plots
legend.row2 <- get_legend(
  # create some space to the left of the legend
  g_vis_gr + labs(colour='Visible minorities\n(Quintiles)', fill='Visible minorities\n(Quintiles)') + theme(legend.box.margin = margin(0, 0, 0, 12))
)

prow2.1 <- plot_grid(
  g_vis_bk.hrdl + xlab("% Bike lane to streets 2011") + ylab("% Bike lane to streets 2016") + theme(legend.position = "none"),
  g_vis_gr + xlab("% green space within CT 2011") + ylab("% green space within CT 2016") + theme(legend.position = "none"),
  g_vis_tc + xlab("% tree canopy within CT 2011") + ylab("% tree canopy within CT 2016") + theme(legend.position = "none"),
  align = "vh",
  labels = c("D", "E", "F"),
  hjust = -1,
  nrow = 1
)

prow2 <- plot_grid(prow2.1, legend.row2, rel_widths = c(3, .4))

# extract the legend from one of the plots
legend.row3 <- get_legend(
  # create some space to the left of the legend
  g_gen_gr + labs(colour='Gentrified', fill='Gentrified') + theme(legend.box.margin = margin(0, 0, 0, 12))
)

prow3.1 <- plot_grid(
  g_gen_bk.hrdl + xlab("% Bike lane to streets 2011") + ylab("% Bike lane to streets 2016") + theme(legend.position = "none"),
  g_gen_gr + xlab("% green space within CT 2011") + ylab("% green space within CT 2016") + theme(legend.position = "none"),
  g_gen_tc + xlab("% tree canopy within CT 2011") + ylab("% tree canopy within CT 2016") + theme(legend.position = "none"),
  align = "vh",
  labels = c("G", "H", "I"),
  hjust = -1,
  nrow = 1
)

prow3 <- plot_grid(prow3.1, legend.row3, rel_widths = c(3, .4))

# output all graphs
plot_grid(prow1, prow2, prow3, ncol=1)

12 Annexes

## R version 4.1.2 (2021-11-01)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Big Sur 10.16
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_CA.UTF-8/en_CA.UTF-8/en_CA.UTF-8/C/en_CA.UTF-8/en_CA.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] cancensus_0.5.0  stringr_1.4.0    DHARMa_0.4.5     stargazer_5.2.2 
##  [5] spaMM_3.10.0     cachem_1.0.6     memoise_2.0.1    spatialreg_1.2-1
##  [9] spdep_1.2-2      spData_2.0.1     sp_1.4-6         lme4_1.1-28     
## [13] Matrix_1.4-0     cowplot_1.1.1    biscale_0.2.0    openxlsx_4.2.5  
## [17] RPostgres_1.4.3  DBI_1.1.2        ggmap_3.0.0      ggplot2_3.3.5   
## [21] stars_0.5-5      abind_1.4-5      sf_1.0-6         tidyr_1.2.0     
## [25] dplyr_1.0.8     
## 
## loaded via a namespace (and not attached):
##   [1] ggnewscale_0.4.7    minqa_1.2.4         colorspace_2.0-3   
##   [4] rjson_0.2.21        deldir_1.0-6        ellipsis_0.3.2     
##   [7] class_7.3-20        rstudioapi_0.13     proxy_0.4-26       
##  [10] farver_2.1.0        bit64_4.0.5         fansi_1.0.2        
##  [13] lubridate_1.8.0     xml2_1.3.3          codetools_0.2-18   
##  [16] splines_4.1.2       knitr_1.37          jsonlite_1.8.0     
##  [19] nloptr_2.0.0        png_0.1-7           compiler_4.1.2     
##  [22] httr_1.4.2          assertthat_0.2.1    fastmap_1.1.0      
##  [25] cli_3.2.0           s2_1.0.7            htmltools_0.5.2    
##  [28] tools_4.1.2         coda_0.19-4         gtable_0.3.0       
##  [31] glue_1.6.2          wk_0.6.0            gmodels_2.18.1     
##  [34] Rcpp_1.0.8          slam_0.1-50         jquerylib_0.1.4    
##  [37] raster_3.5-15       vctrs_0.3.8         svglite_2.1.0      
##  [40] gdata_2.18.0        nlme_3.1-155        lwgeom_0.2-8       
##  [43] xfun_0.29           rvest_1.0.2         lifecycle_1.0.1    
##  [46] gtools_3.9.2        terra_1.5-21        ROI_1.0-0          
##  [49] LearnBayes_2.15.1   MASS_7.3-55         scales_1.1.1       
##  [52] hms_1.1.1           parallel_4.1.2      expm_0.999-6       
##  [55] RColorBrewer_1.1-2  yaml_2.3.5          pbapply_1.5-0      
##  [58] sass_0.4.0          stringi_1.7.6       highr_0.9          
##  [61] e1071_1.7-9         boot_1.3-28         zip_2.2.0          
##  [64] systemfonts_1.0.4   RgoogleMaps_1.4.5.3 rlang_1.0.1        
##  [67] pkgconfig_2.0.3     bitops_1.0-7        evaluate_0.15      
##  [70] lattice_0.20-45     purrr_0.3.4         labeling_0.4.2     
##  [73] bit_4.0.4           tidyselect_1.1.2    geojsonsf_2.0.1    
##  [76] plyr_1.8.6          magrittr_2.0.2      R6_2.5.1           
##  [79] generics_0.1.2      mgcv_1.8-39         pillar_1.7.0       
##  [82] withr_2.4.3         units_0.8-0         tibble_3.1.6       
##  [85] crayon_1.5.0        KernSmooth_2.23-20  utf8_1.2.2         
##  [88] rmarkdown_2.11      jpeg_0.1-9          grid_4.1.2         
##  [91] blob_1.2.2          webshot_0.5.2       digest_0.6.29      
##  [94] classInt_0.4-3      numDeriv_2016.8-1.1 munsell_0.5.0      
##  [97] viridisLite_0.4.0   kableExtra_1.3.4    registry_0.5-1     
## [100] bslib_0.3.1